Quiz about Deriving and Using the Equation of a Circle

Question 1

Given the equation of a circle $$x^2+y^2-10x+16y-30=0$$
Check all of the statements that are true.

Accepted Answer

$$\left(x-5\right)^2+\left(y+8\right)^{2\ }=119$$

Accepted Answer

Center is (5, -8) Radius= 10.9

Answer

Center is (-5, 8) Radius is = 10.9

Answer

$$\left(x+5\right)^2+\left(y-8\right)^2=119$$

Question 2

What is the equation of the circle?

Accepted Answer

$$x^2+y^2+2x+2y-7=0$$

Answer

$$x^2+y^2+2x+2y-1=0$$

Answer

$$x^2+y^2+2x-2y-1=0$$

Answer

$$x^2+y^2-2x-2y-7=0$$

Question 3

Write the standard form of the equation of a circle with center (0,0) and radius 8.

Accepted Answer

$$x^2+y^2=64$$

Answer

$$x^2+y^2=8$$

Answer

$$x^2+y^2=\sqrt{8}$$

Answer

$$x^2+y^2=16$$

Question 4

Write the circle equation

Accepted Answer

(x-2)²+(y+2)²=361

Answer

(x+2)²+(y-2)²=361

Answer

(x+2)²+(y-2)²=19

Answer

(x-2)²+(y+2)²=19

Question 5

Find the graph to this equation

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 6

Find the center and radius of the circle: 3x²+ 3y²+ 42x - 6y = -3

Accepted Answer

center= (-7, 1) radius= 7

Answer

center= (-7, 2) radius= 3

Answer

center= (-4, 1) radius= 5

Question 7

Determine the CENTER of the circle:

Accepted Answer

$$\left(1,-3\right)$$

Answer

$$\left(-1,3\right)$$

Answer

$$\left(-1,-3\right)$$

Answer

$$\left(1,3\right)$$

Question 8

The equation $$\left(x-5\right)^2+\left(y-1\right)^2=r^2$$ represents circle A. The point (9, -2) lies on the circle. What is r, the length of the radius of circle A?

Accepted Answer

$$5$$

Answer

$$1$$

Answer

$$4\sqrt{3}$$

Answer

$$\sqrt{17}$$

Question 9

Give the equation of the circle in standard form.

Accepted Answer

$$\left(x-4\right)^2+y^2=4$$

Answer

$$\left(x+4\right)^2+y^2=4$$

Answer

$$x^2+\left(y-4\right)^2=2$$

Answer

$$\left(x-4\right)^2+y^2=2$$

Question 10

Write the standard form of the equation of a circle with center $$\left(3,-2\right)$$ and a point on the circle is $$\left(23,19\right)$$ .

Accepted Answer

$$\left(x-3\right)^2+\left(y+2\right)^2=841$$

Answer

$$\left(x+3\right)^2+\left(y-2\right)^2=29$$

Answer

$$\left(x-3\right)^2+\left(y+2\right)^2=29$$

Answer

$$\left(x+3\right)^2+\left(y-2\right)^2=841$$

Question 11

The radius of a circle has length 6. The center is at (-5, 2). Give the equation of the circle.

Accepted Answer

(x + 5)²+ (y - 2)²= 36

Answer

(x - 2)²+ (y + 5)²= 36

Answer

(x - 5)² + (y + 2)² = 6

Answer

(x + 2)²+ (y - 5)²= 6

Question 12

Which is the equation of this circle?

Accepted Answer

None of these

Answer

$$\left(x+2\right)^2+\left(y+1\right)^2=1^2$$

Answer

$$\left(x+2\right)^2+\left(y-1\right)^2=2^2$$

Answer

$$\left(x-2\right)^2+\left(y-1\right)^2=4^2$$

Question 13

What is the radius of the circle given by the equation above?

Accepted Answer

7

Answer

49

Answer

2401

Answer

98

Deriving and Using the Equation of a Circle

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