Question

*100 points* A circle has a diameter with endpoints (-7, -1) and (-5, -9).

What is the equation of the circle?

Answer 1

Explanation:

Consider the end points (-7,-1) and (-5,-9)

The center is the mid point between these two points.

The value of center is,

(h,k) = ((-7-5)/2, (-1-9)/2)

(h,k) = (-12/2,-10/2)

(h,k) = (-6, -5)

If the center (h,k) = (-6, -5) and radius is r then the equation of the circle is,

Equation of Circle,

((x-h)^2)+((y-k)^2) = r^2

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

Hence, the answer is ((x+6)^2)+(y+5)^2 = r^2.

Answer 2

Diameter

• √(-7+5)²+(-1+9)²
• √2²+8²
• √4+64
• √68
• 2√17

Radius

• 2√17/2
• √17units

Now

Centre

(h,k)

• (-7-5/2,-1-9/2)
• (-12/2,-10/2)
• (-6,-5)

Equation

• (x-h)²+(y-k)²=r²
• (x+6)²+(y+5)²=(√17)²
• (x+6)²+(y+5)²=17

Option A