Find the equation of a circle whose center is at the point (-2 , 3) and its diameter has a length of 10.

Question

Find the equation of circle

Answer 1

Center of the circle is (-2, 3)

Diameter  =  10

Radius (r) =  10/2  =  5

The standard form of the circle equation is ( x - h )² + ( y - k )² = r², where, (h, k) is the center of the circle, and r is the radius.

Substitute (h, k)  =  (-2, 3)  and r  =  5 in above standard form

(x + 2)^2  +  (y - 3)^2  =  5^2

x^2 + 4x + 4  +  y^2 - 6y + 9  =  25

x^2 + 4x + 4  +  y^2 - 6y + 9 - 25  =  0

x^2  +  y^2 + 4x - 6y - 12  =  0

Answer :

The equation of the circle is x^2  +  y^2 + 4x - 6y - 12  =  0.