Question

A circle has a center at (-2, 5) and a radius of bold 3 square root of bold 2units. What is the equation of the circle in standard form?

Answer 1

Given:

The center of the circle = (-2,5)

The radius of the circle = $3\sqrt{2}$ units.

To find:

The equation of the circle is standard form.

Solution:

The standard form of a circle is:

$(x-h)^2+(y-k)^2=r^2$               ...(i)

Where, (h,k) is the center of the circle and r is the radius of the circle.

It is given that the center of the circle is (-2,5). So, $h=-2,\ k=5$.

The radius of the circle is $3\sqrt{2}$ units. So, $r=3\sqrt{2}$.

Putting $h=-2,\ k=5$ and $r=3\sqrt{2}$ in (i), we get

$(x-(-2))^2+(y-(5))^2=(3\sqrt{2})^2$

$(x+2)^2+(y-5)^2=18$

Therefore, the equation of the circle is $(x+2)^2+(y-5)^2=18$.