Question

The equation of a circle is (x-3)^2+(y+2)^2=25. The point (8,-2) is on the circle. What is the equation of the line that is tangent to the circles at (8,-2)?

Answer 1

From the equation, you can see that (3,-2) is the center of the circle (the terms are 0 for those x,y values). The mentioned point has the same y value as the center. That's good news because it tells us that the tangent line is exactly vertical. The x coordinate is given as x=8. Vertical lines have an equation of x=... so x=8 is the right answer.

Answer 2

If you need only answer it's x = 8.