Quiz about Equation of Circle

Question 1

A circle in the xy-plane has the equation shown. What is the x-coordinate of the center of the circle? $$(x + 20)^2 + (y - 30)^2 = 225$$

Accepted Answer

-20

Answer

30

Answer

20

Answer

-30

Question 2

Find the center of the circle $$x^2+y^2+4x-8y-5=0$$ .

Accepted Answer

Centre = (-2, 4)

Answer

Centre = (2, 6)

Answer

Centre = (2, -4)

Answer

Centre = (-2, -4)

Answer

Centre = (2, 4)

Question 3

Find the equation of the circle with center (-1, 2) and radius = 2 units.

Accepted Answer

Option 2 and Option 3

Answer

$$option\ 2:\ (x+1)^2+(y-2)^2=2^2$$

Answer

Option 3: $$x^2 + 2x + y^2 - 4y + 1 = 0$$

Answer

Option 1 and Option 3

Answer

Option 1: $$(x - 1)^2 + (y - 2)^2 = 2^2$$

Question 4

The equation $$x^2 + y^2 - 12x - 8y + 27 = 0$$ is equivalent to:

Accepted Answer

$$(x - 6)^2 + (y - 4)^2 = 25$$

Answer

$$(x + 6)^2 + (y + 4)^2 = 25$$

Answer

$$(x - 6)^2 + (y - 4)^2 = 27$$

Answer

$$(x + 6)^2 + (y + 4)^2 = 3\sqrt{3}$$

Question 5

Write the equation of the circle. (Assume a radius of integer length.)

Accepted Answer

$$(x-5)^2+(y-6)^2=9$$

Answer

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

Answer

$$x^2+y^2+2gx+2fy+c=0$$

Answer

$$(x+6)^2+(y+5)^2=r^2$$

Question 6

In the equation $$(x-4)^2+(y-3)^2=25$$ , the center of the circle is at...

Accepted Answer

(4, 3)

Answer

(-3, -4)

Answer

(3, 4)

Answer

(-4, -3)

Question 7

The diameter of a circle has length 22. The center is at (-5, 2). Give the equation of the circle.

Accepted Answer

$$(x+5)^2+(y-2)^2=121$$

Answer

$$(x-5)^2+(y+2)^2=11$$

Answer

$$(x+2)^2+(y-5)^2=121$$

Answer

$$(x-2)^2+(y+5)^2=22^2$$

Equation of Circle