Question

Determine the equation of the circle with radius 4 and Centre (-2, 3).​

Answer 1

Answer:

Solution:

Given that:

Radius, r = 4, and center (h, k) = (-2, 3).

We know that the equation of a circle with centre (h, k) and radius r is given as

(x – h)2 + (y – k)2 = r2 ….(1)

Now, substitute the radius and center values in (1), we get

Therefore, the equation of the circle is

(x + 2)2+ (y – 3)2 = (4)2

x2+ 4x + 4 + y2 – 6y + 9 = 16

Now, simplify the above equation, we get:

x2 + y2+ 4x – 6y – 3 = 0

Thus, the equation of a circle with center (-2, 3) and radius 4 is x2 + y2+ 4x – 6y – 3 = 0