Pre-calculus - First Semester (1st Quarter)

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Questions and Answers

Which of the following is the standard equation of the circle with center (0, -3) and radius 58?

$x^2 + (y + 3)^2 = 58$ (correct)
$x^2 + (y - 3)^2 = 29$
$x^2 + (y - 3)^2 = 58$
$x^2 + (y + 3)^2 = 29$

Which of the following is the standard equation of a circle with center (3, -2) and radius 2?

$(x + 3)^2 + (y - 2)^2 = 4$
$(x - 3)^2 + (y + 2)^2 = 4$
$(x - 3)^2 + (y + 2)^2 = 2$ (correct)
$(x + 3)^2 + (y - 2)^2 = 2$

Which of the following is the standard equation of a circle with center (5, 6) that is tangent to the x-axis?

$(x + 5)^2 + (y + 6)^2 = 36$
$(x - 5)^2 + (y + 6)^2 = 36$ (correct)
$(x + 5)^2 + (y - 6)^2 = 36$
$(x - 5)^2 + (y - 6)^2 = 36$

Which of the following is the standard equation of a circle with the center at the origin and a diameter of 6?

$x^2 + y^2 = 36$ (C) Signup and view all the answers

Which of the following is the center and radius of the circle with the equation $x^2 + y^2 + 10x - 14y + 70 = 0$?

Center: (-5, 7), Radius: 5 (A) Signup and view all the answers

Which of the following is the standard equation of a circle with center (0, 0) and radius 11?

$x^2 + y^2 = 121$ (A), $x^2 + y^2 = 121$ (B), $x^2 + y^2 = 121$ (C) Signup and view all the answers

Which of the following is the standard equation of a circle with center (3, -2) and radius 2?

$(x - 3)^2 + (y + 2)^2 = 4$ (C) Signup and view all the answers

Which of the following is the standard equation of a circle with center (5, 6) that is tangent to the x-axis?

$(x - 5)^2 + (y + 6)^2 = 36$ (D) Signup and view all the answers

Which of the following is the standard equation of a circle with center (0, -3) and radius 58?

$x^2 + (y + 3)^2 = 58$ (B) Signup and view all the answers

Which of the following is the standard equation of a circle with center (3, -2) and radius 2?

$(x - 3)^2 + (y + 2)^2 = 4$ (D) Signup and view all the answers

Which of the following is the standard equation of a circle with center (5, 6) that is tangent to the x-axis?

$(x - 5)^2 + (y + 6)^2 = 36$ (D) Signup and view all the answers

Which of the following is the standard equation of a parabola with vertex (3, -4) and focus (3, -2)?

$y = -2(x - 3)^2 - 4$ (C) Signup and view all the answers

Which of the following is the standard equation of a parabola with vertex (-2, 5) and directrix y = 9?

$y = -rac{1}{4}(x + 2)^2 + 5$ (B) Signup and view all the answers

Which of the following is the equation of the axis of symmetry for the parabola with equation $y = 2x^2 + 4x + 3$?

$x = -1$ (A) Signup and view all the answers

Which of the following is the equation of the latus rectum for the parabola with equation $y = rac{1}{4}x^2 - 2x + 1$?

$x = 4$ (A) Signup and view all the answers

Which of the following is the general equation of a parabola with focus (2, -1) and directrix x = -3?

$x^2 = 8y + 6x - 13$ (C) Signup and view all the answers

Which of the following is the equation of the axis of symmetry for a parabola with vertex (2, -5)?

$x = 2$ (B) Signup and view all the answers

Which of the following is the standard equation of a parabola with vertex (0, 0) and directrix y = -4?

$y^2 = -8x$ (D) Signup and view all the answers

Which of the following is the standard equation of a circle with center (-3, 2) and radius 5?

$(x + 3)^2 + (y - 2)^2 = 25$ (B) Signup and view all the answers

Which of the following is the standard equation of a parabola with vertex (2, -3) and directrix y = 5?

$x^2 - 4x + 24y + 17 = 0$ (C) Signup and view all the answers

Which of the following is the equation of the latus rectum for the parabola with equation $y = -3x^2 + 6x - 1$?

$x = 2$ (B) Signup and view all the answers

Which of the following is the equation of the axis of symmetry for the parabola with equation $y = 2x^2 - 4x + 3$?

$x = -1$ (B) Signup and view all the answers

Which of the following is the standard form equation of the given ellipse?

$\frac{(x-0)^2}{18^2} + \frac{(y-0)^2}{15^2} = 1$ (D) Signup and view all the answers

What is the maximum height of the truck?

14.14 ft (A) Signup and view all the answers

Which of the following is the equation of an ellipse with a major axis along the x-axis and a center at (h, k)?

$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$ (C) Signup and view all the answers

Which of the following is the equation of an ellipse with a major axis along the y-axis and a center at (h, k)?

$\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1$ (A) Signup and view all the answers

What is the equation of the ellipse with the given standard form equation?

$\frac{(x-6)^2}{18^2} + \frac{(y-n)^2}{15^2} = 1$ (D) Signup and view all the answers

Which of the following is the standard equation of an ellipse with a major axis along the x-axis and a center at (h, k)?

$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$ (C) Signup and view all the answers

What are the coordinates of the foci of the ellipse with the equation $x^2/81 + y^2/25 = 1$?

(±7, 6) (C) Signup and view all the answers

What is the equation of the ellipse with the given standard form equation?

$\frac{(x-4)^2}{16} + \frac{(y-2)^2}{9} = 1$ (A) Signup and view all the answers

Which of the following is the standard equation of an ellipse with a major axis along the x-axis and a center at (h, k)?

$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$ (C) Signup and view all the answers

Which of the following is the equation of an ellipse with a major axis along the y-axis and a center at (h, k)?

$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$ (A) Signup and view all the answers

What is the maximum height of the truck?

14.14 ft (D) Signup and view all the answers

Which of the following is the standard form of the equation given in the text?

$(x+3)^2/4 - (y+1)^2/1 = 1$ (D) Signup and view all the answers

What is the value of $c$ in the equation $(x-4)^2/15 - (y+3)^2/25 = 1$?

3 (B) Signup and view all the answers

What is the equation of the asymptotes for the hyperbola with the equation $(x-4)^2/15 - (y+3)^2/25 = 1$?

$y = 3x/5 + 4/5$ (C) Signup and view all the answers

What is the value of $b^2$ in the equation $6x^2 - 5y^2 = 30$?

6 (A) Signup and view all the answers

What is the equation of the latus rectum for the parabola with equation $y = -3x^2 + 6x - 1$?

$x = 2/3$ (A) Signup and view all the answers

Which of the following is the standard equation of a hyperbola with foci at F1 (600, 0) and F2 (600, 0)?

$\frac{(x-600)^2}{244400} - \frac{y^2}{115600} = 1$ (C) Signup and view all the answers

What is the value of $b^2$ in the equation $(x-4)^2/15 - (y+3)^2/25 = 1$?

25 (D) Signup and view all the answers

What are the coordinates of the center, foci, vertices, and asymptotes of the hyperbola with the equation $(x-4)^2/15 - (y+3)^2/25 = 1$?

Center: (4, -3), Foci: (4±√40, -3), Vertices: (4±√15, -3), Asymptotes: y = ±(5/3)(x-4) - 3 (C) Signup and view all the answers

Which of the following is the standard equation of a hyperbola with foci at F1 (600, 0) and F2 (600, 0)?

$(x-600)^2/4 - (y-0)^2/1 = 1$ (A) Signup and view all the answers

What are the coordinates of the foci of the ellipse with the equation $x^2/81 + y^2/25 = 1$?

(0, -5) (B) Signup and view all the answers

What is the value of $c$ in the equation $(x-4)^2/15 - (y+3)^2/25 = 1$?

5 (C) Signup and view all the answers

Which of the following is the standard equation of an ellipse with a major axis along the x-axis and a center at (h, k)?

$(x-h)^2/a^2 - (y-k)^2/b^2 = 1$ (B) Signup and view all the answers

Which of the following is the equation of the directrix for the parabola with equation $y = 2x^2 - 4x + 1$?

$y = -1$ (B) Signup and view all the answers

Which of the following is the standard equation of a hyperbola with foci at F1 (0, 3) and F2 (0, -3)?

$y^2/a^2 - x^2/b^2 = 1$ (B) Signup and view all the answers

Which of the following is the equation of the latus rectum for the parabola with equation $y = 4x^2 + 8x + 2$?

$x = -2$ (D) Signup and view all the answers

Which of the following is the standard equation of a parabola with vertex (3, -2) and directrix y = -6?

$(x+3)^2 = 4p(y-2)$ (C) Signup and view all the answers

Which of the following is the standard equation of a circle with center (-3, 2) and radius 5?

$(x + 3)^2 + (y - 2)^2 = 5^2$ (A) Signup and view all the answers

Which of the following is the standard equation of a hyperbola with foci at F1 (0, 3) and F2 (0, -3)?

$x^2 - y^2 = 9$ (B) Signup and view all the answers

Which of the following is the general equation of a parabola with focus (2, -1) and directrix x = -3?

$(x - 2)^2 = 4p(y + 1)$ (D) Signup and view all the answers

Which of the following is the standard equation of a circle with center (0, -3) and radius 58?

$x^2 + (y + 3)^2 = 58^2$ (C) Signup and view all the answers

Which of the following is the standard equation of an ellipse with a major axis along the y-axis and a center at (h, k)?

$\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1$ (A) Signup and view all the answers

What is the maximum height of the truck?

16 feet (A) Signup and view all the answers

Which of the following is the standard equation of a circle with center (0, 0) and radius 11?

$x^2 + y^2 = 121$ (B) Signup and view all the answers

Which of the following is the standard equation of the circle with center (0, -3) and radius 58?

$x^2 + (y+3)^2 = 58^2$ (A) Signup and view all the answers

Which of the following equations represents a linear equation?

$3x + 2y = 5$ (A) Signup and view all the answers

Which of the following equations represents a non-linear equation?

$x^2 + y^2 = 25$ (C) Signup and view all the answers

What is the slope of the line represented by the equation $2x + 3y = 7$?

$\frac{2}{3}$ (D) Signup and view all the answers

What is the constant value in the linear equation $4x - 5y = 10$?

10 (D) Signup and view all the answers

Which of the following equations represents a non-linear equation?

$x^2 + y^2 = 16$ (B) Signup and view all the answers

Which of the following equations represents a linear equation?

$10x = 1$ (C) Signup and view all the answers

Which of the following equations represents a non-linear equation?

$x^2 + 12xy + y^2 = 0$ (B) Signup and view all the answers

What is the general representation of a linear equation?

$y = mx + c$ (D) Signup and view all the answers

Which of the following equations represents a linear equation?

$4x = 3x$ (A) Signup and view all the answers

Which of the following equations represents a non-linear equation?

$x^2 + y^2 = 1$ (D) Signup and view all the answers

What is the standard equation of a linear equation?

$y = mx + c$ (B) Signup and view all the answers

Flashcards

Circle Equation

Standard equation: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.

Origin-centered circle

The standard equation of a circle with center (0,0) and radius r is x^2 + y^2 = r^2.

Axis of Symmetry

A line that intersects the parabola at the vertex and divides it into two symmetrical halves.

Latus Rectum

A line segment through the focus, perpendicular to the axis of symmetry, with endpoints on the parabola.