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Questions and Answers
Which conic section is represented by the equation $3x^2 + 4y^2 - 12x + 16y - 20 = 0$?
Which conic section is represented by the equation $3x^2 + 4y^2 - 12x + 16y - 20 = 0$?
- Ellipse (correct)
- Hyperbola
- Circle
- Parabola
Which of the following represents the equation of a straight line passing through the point (3, 4) and perpendicular to the line $2x - 3y + 5 = 0$?
Which of the following represents the equation of a straight line passing through the point (3, 4) and perpendicular to the line $2x - 3y + 5 = 0$?
- $2x + 3y - 1 = 0$
- $2x - 3y - 11 = 0
- $3x + 2y - 5 = 0$
- $3x - 2y - 5 = 0$ (correct)
For the circle with center (2, -3) and passing through the point (4, 1), what is the equation of the circle?
For the circle with center (2, -3) and passing through the point (4, 1), what is the equation of the circle?
- $(x - 2)^2 + (y + 3)^2 = 20$
- $(x - 4)^2 + (y - 1)^2 = 20$
- $(x - 2)^2 + (y + 3)^2 = 16$ (correct)
- $(x - 4)^2 + (y - 1)^2 = 16$
What is the equation of the tangent to the circle $x^2 + y^2 - 6x + 8y - 5 = 0$ at the point (1, -1)?
What is the equation of the tangent to the circle $x^2 + y^2 - 6x + 8y - 5 = 0$ at the point (1, -1)?
Find the equation of the ellipse with foci at (1, 2) and (-1, 2) passing through the point (3, 2).
Find the equation of the ellipse with foci at (1, 2) and (-1, 2) passing through the point (3, 2).
Determine the equation of the parabola with focus at (3, 4) and directrix $y = -2$.
Determine the equation of the parabola with focus at (3, 4) and directrix $y = -2$.
Given the equation of the hyperbola $9x^2 - 16y^2 - 36x + 64y - 71 = 0$, find the coordinates of the center and vertices.
Given the equation of the hyperbola $9x^2 - 16y^2 - 36x + 64y - 71 = 0$, find the coordinates of the center and vertices.
The equation of the tangent to the circle $x^2 + y^2 - 6x + 8y - 5 = 0$ at the point (1, -1) is a ______ line
The equation of the tangent to the circle $x^2 + y^2 - 6x + 8y - 5 = 0$ at the point (1, -1) is a ______ line
Find the equation of the ______ with foci at (1, 2) and (-1, 2) passing through the point (3, 2)
Find the equation of the ______ with foci at (1, 2) and (-1, 2) passing through the point (3, 2)
Determine the equation of the ______ with focus at (3, 4) and directrix $y = -2$
Determine the equation of the ______ with focus at (3, 4) and directrix $y = -2$
For the circle with center (2, -3) and passing through the point (4, 1), what is the equation of the ______?
For the circle with center (2, -3) and passing through the point (4, 1), what is the equation of the ______?
Flashcards
Ellipse
Ellipse
A conic section that is oval-shaped. In standard form, it involves the sum of squared x and y terms with different denominators.
Perpendicular Lines
Perpendicular Lines
A line that intersects another line at a right angle (90 degrees). Slopes are negative reciprocals.
Circle Equation
Circle Equation
A set of points equidistant from a center. Equation: (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center and r is the radius.
Tangent Line
Tangent Line
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Ellipse Definition
Ellipse Definition
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Parabola Definition
Parabola Definition
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Hyperbola Center
Hyperbola Center
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Straight
Straight
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Ellipse
Ellipse
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Parabola
Parabola
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Circle
Circle
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Study Notes
Conic Sections
- The equation $3x^2 + 4y^2 - 12x + 16y - 20 = 0$ represents an ellipse.
Lines
- The equation of a line perpendicular to $2x - 3y + 5 = 0$ passing through (3, 4) is $3x + 2y - 17 = 0$.
Circles
- The equation of a circle with center (2, -3) and passing through (4, 1) is $(x - 2)^2 + (y + 3)^2 = 25$.
- The equation of the tangent to $x^2 + y^2 - 6x + 8y - 5 = 0$ at (1, -1) is $x - 4y - 3 = 0$.
Ellipses
- The equation of the ellipse with foci (1, 2) and (-1, 2) and passing through (3, 2) is $\frac{(x - 1)^2} {9} + \frac{(y - 2)^2}{5} = 1$.
Parabolas
- The equation of the parabola with focus (3, 4) and directrix $y = -2$ is $(x - 3)^2 = 12(y - 1)$.
Hyperbolas
- The center of the hyperbola $9x^2 - 16y^2 - 36x + 64y - 71 = 0$ is (2, 2).
- The vertices of the hyperbola are (2, 2 ± √5).
Tangent Lines
- The equation of the tangent to the circle $x^2 + y^2 - 6x + 8y - 5 = 0$ at the point (1, -1) is a linear line.
Ellipses Notes
- Find the equation of the ellipse with foci at (1, 2) and (-1, 2) passing through the point (3, 2)
Parabolas Notes
- Determine the equation of the parabola with focus at (3, 4) and directrix $y = -2$
Circles Notes
- For the circle with center (2, -3) and passing through the point (4, 1), what is the equation of the circle?
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Description
This unit test paper consists of 25 marks and covers topics such as straight lines, circle, conic section, set, and relation. Test your understanding of these mathematical concepts with this comprehensive assessment.
