Quiz about Conic Sections - Circle

Question 1

Which of the following represents the standard form of the equation of a circle?

Accepted Answer

$$(𝑥−ℎ)^2+(𝑦−𝑘)^2=𝑟^2$$

Answer

$$(x−h)^2+(y−k)^2=r$$

Answer

$$x^2+y^2+Dx+Ey+F=0$$

Answer

$$Ax^2+By^2+C=0$$

Question 2

The center of the circle given by the equation $$\left(x+4\right)^2+\left(y-1\right)^2=16$$ is:

Accepted Answer

$$\left(-4,1\right)$$

Answer

$$\left(4,-1\right)$$

Answer

$$\left(1,4\right)$$

Answer

$$\left(-1,4\right)$$

Question 3

The radius of the circle given by the equation $$\left(x-2\right)^2+\left(y+3\right)^2=25$$ is:

Accepted Answer

5

Answer

10

Answer

25

Answer

2

Question 4

Which of the following represents a circle centered at the origin with radius 6?

Accepted Answer

$$x^2+y^2=36$$

Answer

$$x^2+y^2=12$$

Answer

$$\left(x+6\right)+\left(y+6\right)^2=0$$

Answer

$$\left(x-6\right)+\left(y-6\right)^2=36$$

Question 5

Which of the following is not a property of a circle?

Accepted Answer

The circumference is the same as the area.

Answer

All radii are equal.

Answer

A diameter is twice the length of the radius.

Answer

The center is equidistant from all points on the circle.

Question 6

Which of the following equations represents a circle with center (0,0) and radius 8?

Accepted Answer

$$𝑥^2+𝑦^2=64$$

Answer

$$𝑥^2+𝑦^2=16$$

Answer

$$\left(x+8\right)^2+\left(y+8\right)^2=64$$

Answer

$$\left(x-8\right)^2+\left(y-8\right)^2=64$$

Question 7

Convert the standard form equation $$(𝑥−1)^2+(𝑦−2)^2=9$$ to the general form.

Accepted Answer

$$𝑥^2+𝑦^2−2𝑥−4𝑦-4=0$$

Answer

$$𝑥^2+𝑦^2−2𝑥−4𝑦+1=0$$

Answer

$$𝑥^2+𝑦^2−2𝑥−4𝑦+5=0$$

Answer

$$𝑥^2+𝑦^2−2𝑥−4𝑦-12=0$$

Question 8

Convert the general form equation $$𝑥^2+𝑦^2−4𝑥+6𝑦−12=0$$ to the standard form.

Accepted Answer

$$(𝑥−2)^2+(𝑦+3)^2=25$$

Answer

$$(𝑥−2)^2+(𝑦−3)^2=16$$

Answer

$$(𝑥+2)^2+(𝑦−3)^2=16$$

Answer

$$(𝑥+2)^2+(𝑦+3)^2=25$$

Question 9

What is the center of the circle with the equation $$x^2+y^2−6x+8y+9=0$$ ?

Accepted Answer

$$\left(3,-4\right)$$

Answer

$$\left(3,4\right)$$

Answer

$$\left(4,-3\right)$$

Answer

$$\left(1,2\right)$$

Question 10

What is the center of the circle given by the equation $$(x−7)^2+(y+1)^2=36$$

Accepted Answer

$$\left(7,-1\right)$$

Answer

$$\left(-7,-1\right)$$

Answer

$$\left(1,-7\right)$$

Answer

$$\left(-1,7\right)$$

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