SOLUTION: 1.) the circle is tangent to the line y=3-5x at the point (2,-7) whose center is on the line x= 2y+19. find the equation of the circle and illustrate .

Question 1142413: 1.) the circle is tangent to the line y=3-5x at the point (2,-7) whose center is on the line x= 2y+19. find the equation of the circle and illustrate .
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Since the circle is tangent to the line y=-5x+3 at the point (2,-7), the line through (2,-7) perpendicular to the line y=-5x+3 passes through the center of the circle.

You also know the center of the circle is on the line x = 2y+19.

So you know the equations of two lines that both contain the center of the circle.

(1) Find the equation of the line perpendicular to y=-5x+3 passing through (2,-7).
(2) Find the common solution of the two lines containing the center of the circle.
(3) Use the distance formula to find the radius of the circle (the distance from (2,-7) to the center of the circle).
(4) Plug the known center and radius of the circle in the standard equation of a circle,
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