Find an equation of a circle

Question

Find an equation of the circle whose diameter has endpoints (−3,−6) and (1,2)

Answer 1

The center of the circle is the midpoint of the diameter.

 

    Center = ( (-3+1)/2, (-6+2)/2) = (-1, -2)

 

Radius = Distance from the center to either endpoint of the diameter

 

           = √ [(1-(-1))² + (2-(-2))²] = √[4+16] = √20

 

Equation of circle:  (x-h)² + (y-k)² = r², where (h,k) is the center and r is the radius.

 

So, equation of circle is (x+1)² + (y+2)² = 20

 

Answer 2

Can use P theorem.  Draw a sketch of this line.

 

The line in question is a right triangle' hypotenuse, so 4^2 + 8^2 = x^2, where x is length of line.

 

4 is the difference between -3 and 1; 8 is the difference between -6 and 2.

 

I think you can solve it now.