Find the standard form of the equation of the circle with center (-5,3) and tangent to the line y = 1.

( x + 5 )^2 + ( y - 3 )^2 = 2^2

Step-by-step explanation:

The equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2.

We know that h=-5 and k=3, so we just need to solve for r.

To do that, we need to envision the circle on a graph. If the edge of the circle touches the horizontal line y=1, how many units is it between the edge of the circle and the middle of the circle?

The middle of the circle is at y=3, and the edge is at y=1, so there are 2 units between the edge and the middle. Which means r=2.

so, ( x + 5 )^2 + ( y - 3 )^2 = 2^2.