Question

Find the equation of a circle that has its center at (-4, 3) and has a radius of 5.

Answer 1

hello :
an equation of the circle Center at the A(a,b) and ridus : r is :
(x-a)² +(y-b)² = r²
in this exercice : a =-4 and b = 3 (Center at the A) r=5
the equation is : (x+4)² +(y-3)² = 25

Answer 2

The resulting equation of the circle is x²+y²+8x-9y = 0

Explanation:

The general form of equation of a circle is represented as:

(x-a)²+(y-b)² = r² with center (a,b) and radius r

Given the centre of (-4,3) and radius of 5

a = -4, b = 3, r = 5

Substituting this value into the general equation of a circle we have:

(x-(-4))²+(y-3)² = 5²

(x+4)²+(y-3)² = 5²

On expansion:

x²+8x+16+y²-9x+9 = 25

x²+y²+8x-9y+16+9-25 = 0

x²+y²+8x-9y = 0