Question 1

Given the endpoints of a diameter of a circle at $$(2, 4)$$ and $$(10, 12)$$, what are the coordinates of the center of the circle?

Accepted Answer

$$(6, 8)$$

Question 2

What is the radius of the circle with endpoints of a diameter at $$(2, 4)$$ and $$(10, 12)$$?

Accepted Answer

$$4\sqrt{2}$$

Question 3

What is the standard form equation of the circle with center $$(6, 8)$$ and radius $$4\sqrt{2}$$?

Accepted Answer

$$(x-6)^2$$ + $$(y-8)^2 = 32$

Question 4

Which of the following is the equation of an ellipse centered at $$(2, -1)$$ with a vertical major axis, $$a = 5$$, and $$b = 3$$?

Accepted Answer

$$\frac{(x-2)^2$}{9} + \frac{(y+1)^2$}{25} = 1$$

Question 5

For the ellipse $$\frac{(x-1)^2$}{16} + \frac{(y+2)^2$}{9} = 1$$, what are the coordinates of the foci?

Accepted Answer

$$(1 \pm \sqrt{7}, -2)$$

Question 6

Which of the following best describes the orientation and center of the hyperbola $$\frac{(y-1)^2$}{9} - \frac{(x+2)^2$}{16} = 1$$?

Accepted Answer

Vertical orientation, center at $$(-2, 1)$$

Question 7

What is the equation of the asymptotes for the hyperbola $$\frac{(x-3)^2$}{25} - \frac{(y+1)^2$}{9} = 1$$?

Accepted Answer

$$y + 1 = \pm \frac{3}{5}(x - 3)$$

Question 8

A parabola has its vertex at $$(2, -3)$$ and opens upward with $$p = 4. $$What is its equation?

Accepted Answer

$$(x-2)^2 = 16(y+3$$)$$

Question 9

For the parabola $$(y-1)^2 = 8(x+2$$)$$, what are the coordinates of the focus?

Accepted Answer

$$(0, 1)$$

Question 10

Which conic section is defined as the set of all points such that the sum of the distances from two fixed points is constant?

Accepted Answer

Ellipse

Question 11

Given the hyperbola $$\frac{(x-1)^2$}{9} - \frac{(y+2)^2$}{16} = 1$$, what is the distance between its vertices?

Accepted Answer

$$6$$

Question 12

A satellite dish is shaped like a paraboloid. If the vertex is at the origin and the focus is at $$(0, 2)$$, what is the equation of the parabola?

Accepted Answer

$$x^2 = 8y$

Question 13

Which of the following is the equation of a circle with center $$(-3, 5)$$ and passing through the point $$(1, 2)$$?

Accepted Answer

$$(x+3)^2$$ + $$(y-5)^2 = 25$

Question 14

For the ellipse $$\frac{(x-4)^2$}{36} + \frac{(y+1)^2$}{25} = 1$$, what is the length of the major axis?

Accepted Answer

$$12$$

Conic Sections: Circles, Ellipses, Hyperbolas, and Parabolas – Precalculus Study Notes

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