Question 1

Which of the following equations represents a circle in standard form?

Accepted Answer

$$x^2$$ + $$y^2 - 8x + 10y + 25 = 0$

Question 2

Given the equation $$x^2 - 4y - 8x = 8$, what type of conic section does it represent?

Accepted Answer

Parabola

Question 3

Which of the following equations represents a hyperbola centered at the origin?

Accepted Answer

$$\dfrac{x^2$}{25} - \dfrac{y^2$}{16} = 1$$

Question 4

A satellite dish is shaped like a paraboloid. If its cross-section is modeled by $$y^2 = 8x$, what are the coordinates of its vertex?

Accepted Answer

$$(0, 0)$$

Question 5

Which equation matches the graph of a circle centered at $$(2, -3)$$ with radius $$5$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 25$$

Question 6

Given the equation $$9x^2$$ - $$16y^2 - 54x - 160y - 461 = 0$, what type of conic section does it represent?

Accepted Answer

Hyperbola

Question 7

Which of the following is the standard form of the equation $$x^2 + 6x$$ + $$y^2 - 8y = -9$?

Accepted Answer

$$(x + 3)^2$ + (y - 4)^2$ = 20$$

Question 8

A medical imaging device uses the equation $$\dfrac{(x-2)^2$}{9} + \dfrac{(y+1)^2$}{16} = 1 to $$describe a cross-section. What is the center of the ellipse?

Accepted Answer

$$(2, -1)$$

Question 9

Which of the following equations represents a parabola opening to the right?

Accepted Answer

$$y^2 = 8x$

Question 10

Given the equation $$\dfrac{x^2$}{25} + \dfrac{y^2$}{9} = 1$$, what are the lengths of the major and minor axes?

Accepted Answer

Major axis: $$10$$, Minor axis: $$6$$

Question 11

A bridge arch is modeled by $$y = -0.5x^2$ + 4. $$What is the maximum height of the arch?

Accepted Answer

$$4$$

Question 12

Which of the following equations represents a hyperbola opening up and down?

Accepted Answer

$$\dfrac{y^2$}{16} - \dfrac{x^2$}{9} = 1$$

Question 13

A flashlight reflector is shaped like a paraboloid. If its cross-section is $$x^2 = 4y$, what is the focus of the parabola?

Accepted Answer

$$(0, 1)$$

Question 14

Which of the following equations represents an ellipse with center at $$(0, 0)$$ and major axis along the $$y-$$axis?

Accepted Answer

$$\dfrac{x^2$}{9} + \dfrac{y^2$}{16} = 1$$

Question 15

Given the equation $$y = 2x^2$ - 8x + 5$$, what are the coordinates of the vertex?

Accepted Answer

$$(2, -3)$$

Question 16

Which of the following best describes the graph of $$x^2$$ + $$y^2 = 16$?

Accepted Answer

A circle with center at $$(0, 0)$$ and radius $$4$$

Question 17

A satellite moves in an elliptical orbit given by $$\dfrac{(x-3)^2$}{25} + \dfrac{(y+2)^2$}{9} = 1. $$What are the coordinates of the center?

Accepted Answer

$$(3, -2)$$

Question 18

Which of the following equations represents a parabola with vertex at $$(1, -2)$$ opening upward?

Accepted Answer

$$(x - 1)^2$ = 4p(y + 2)$$, $$p \u003e 0$$

Question 19

Given the equation $$x^2$$ - $$y^2 = 9$, what are the coordinates of the vertices of the hyperbola?

Accepted Answer

$$(3, 0)$$ and $$(-3, 0)$$

Question 20

Which of the following equations represents a circle with center at $$(h, k)$$ and radius $$r$$?

Accepted Answer

$$(x - h)^2$ + (y - k)^2$ = r^2$

Conic Sections: Identification, Standard Forms, and Graphs

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