Question

Write the equation in standard form of a circle with center (-9,4), tangent to the y-axis.

Answer 1

`(x+9)^2+(y-4)^2=81`

Explanation:

If the circle has the center at point (a,b) and radius r units, then its equation in standard form is

`(x-a)^2+(y-b)^2=r^2`

In your case, the center of the circle is at point (-9,4). This circle is tangent to the y-axis, then it is tangent to the y-axis at point (0,4). The radius of the circle is the distance between the center and the tangent point:

`r=√((-9-0)^2+(4-4)^2)=√(81+0)=9`

Thus, the equation of the circle is

`(x-(-9))^2+(y-4)^2=9^2\\ \\(x+9)^2+(y-4)^2=81`