Question

What is the diameter of a circle with the equation x2 + y2 - 8x + 2y - 8 = 0?

5 units
6 units
9 units
10 units

Answer 1

50

Explanation:

x2 + y2 - 8x + 2y - 8 = 0

first we find the radius with the equation.

write the equation in standard form.

x2 + y2 - 8x + 2y - 8 = 0

(x-4)^2 + (y+1)^2 = 25

(x-h)² + (y-k)² = r²

this means 25 is the radius and the diameter is two times the radius so,

25 x 2 = 50

Answer 2

Diameter is 10 units

Explanation:

Convert standard form to general form by completing the square:

`x^2+y^2-8x+2y-8=0`

`x^2-8x+y^2+2y-8=0`

`x^2-8x+y^2+2y=8`

`x^2-8x+16+y^2+2y+1=8+16+1`

`(x-4)^2+(y+1)^2=25`

`(x-4)^2+(y+1)^2=5^2`

So, since the radius of the circle is 5 units, then the diameter is twice the radius, which is 10 units.