Answer:
option (a) is correct.
The equation of a circle has its center at (-2, 5) and a radius of 4 units. is ![(x+2)^2+(y-5)^2=16](https://tex.z-dn.net/?f=%28x%2B2%29%5E2%2B%28y-5%29%5E2%3D16)
Step-by-step explanation:
Given : A circle has its center at (-2, 5) and a radius of 4 units.
We have to choose the correct equation representing this given circle.
The general equation of circle with center (h , k) and radius 'r' is given by equation ![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
For the given circle with center at (-2, 5) and a radius of 4 units.
that is h = -2 , k = 5 and r = 4 , we have,
substitute, we have,
![(x-(-2))^2+(y-5)^2=(4)^2](https://tex.z-dn.net/?f=%28x-%28-2%29%29%5E2%2B%28y-5%29%5E2%3D%284%29%5E2)
Simplify , we get,
![(x+2)^2+(y-5)^2=16](https://tex.z-dn.net/?f=%28x%2B2%29%5E2%2B%28y-5%29%5E2%3D16)
Thus, option (a) is correct.
The equation of a circle has its center at (-2, 5) and a radius of 4 units. is ![(x+2)^2+(y-5)^2=16](https://tex.z-dn.net/?f=%28x%2B2%29%5E2%2B%28y-5%29%5E2%3D16)