Algebra 2 - Conic Sections Flashcards

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Questions and Answers

What is a circle?

If $x^2$ and $y^2$ have the same coefficients (correct)

If $x^2$ and $y^2$ do not have the same coefficients, but the same sign

If $x^2$ and $y^2$ have opposite signs

If only one of the two variables are squared

What is an ellipse?

If $x^2$ and $y^2$ do not have the same coefficients, but the same sign (correct)

If $x^2$ and $y^2$ have the same coefficients

If only one of the two variables are squared

If $x^2$ and $y^2$ have opposite signs

What is a hyperbola?

If $x^2$ and $y^2$ have opposite signs (correct)

If $x^2$ and $y^2$ have the same coefficients

If only one of the two variables are squared

If $x^2$ and $y^2$ do not have the same coefficients, but the same sign

What is a parabola?

If only one of the two variables is squared Signup and view all the answers

Find the center of the circle: $(x+8)^2+(y+3)^2=121$.

(-8, -3) Signup and view all the answers

Find the radius of the circle: $(x-5)^2+(y+2)^2=64$.

8 Signup and view all the answers

Find the domain of the circle: $(x-5)^2+(y+2)^2=64$.

[-3, 13] Signup and view all the answers

Find the range of the circle: $(x-5)^2+(y+2)^2=64$.

[-10, 6] Signup and view all the answers

Find the center of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.

(5, -3) Signup and view all the answers

Find the major axis of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.

Vertical Signup and view all the answers

Find the domain of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.

[1, 9] Signup and view all the answers

Find the range of the ellipse: $(x-5)^2/16 + (y+3)^2/25$.

[-8, 2] Signup and view all the answers

Which ways will this hyperbola open? $x^2-y^2=4$.

Left/right Signup and view all the answers

Find the center of the hyperbola: $(x-5)^2/16 - (y+3)^2/144=1$.

(5, -3) Signup and view all the answers

Find the domain of this hyperbola: $(x-5)^2/16 - (y+3)^2/144=1$.

(-infinity, 1] U [9, infinity) Signup and view all the answers

Find the domain of this hyperbola: $(x-5)^2/16 - (y+3)^2/144=1$.

All real numbers Signup and view all the answers

Which way will this parabola open? $2y^2+x+16y+34=0$.

Left Signup and view all the answers

Find the vertex of the parabola: $y=(x+3)^2-4$.

(-3, -4) Signup and view all the answers

Find the domain of the parabola: $y=(x-5)^2$.

All real numbers Signup and view all the answers

Find the range of the parabola: $y=(x-5)^2$.

[0, infinity) Signup and view all the answers

Study Notes

Circle

Defined by the equation where x² and y² have the same coefficients.
Example center for the equation (x+8)²+(y+3)²=121 is (−8,−3).
Radius can be determined from (x−5)²+(y+2)²=64, yielding a radius of 8.

Ellipse

Exists when x² and y² have the same sign but different coefficients.
Center can be found from (x-5)²/16 + (y+3)²/25 as (5,−3).
Major axis is vertical because the larger denominator is associated with (y+3)² (25 > 16).
Domain is [1,9] and range is [-8,2].

Hyperbola

Created when x² and y² have opposite signs.
For the hyperbola x²−y²=4, it opens to the left and right.
Center retrieved from (x-5)²/16 - (y+3)²/144=1 is (5,−3).
Domain is (-∞,1] U [9,∞) and all real numbers for the equation x-5)²/16 - (y+3)²/144=1.

Parabola

Describes the equation with only one variable squared.
Opens left as indicated by the equation 2y²+x+16y+34=0.
Vertex for y=(x+3)²-4 positioned at (-3,−4).
Domain characterized as all real numbers and range as [0,∞) for y=(x-5)².

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Test your knowledge of conic sections in Algebra 2 with these flashcards. Each card defines key terms such as circle, ellipse, hyperbola, and parabola. Perfect for studying or quick reviews before exams.