SOLUTION: The circle is tangent to the line 5x+y=3 at the point (2,-7) and center is on the line x-2y=19. Find the equation of the circle. (I'm struggling to find the center in x-2y=19 that

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Question 1139523: The circle is tangent to the line 5x+y=3 at the point (2,-7) and center is on the line x-2y=19. Find the equation of the circle. (I'm struggling to find the center in x-2y=19 that says to be perpendicular to the center itself and to the point of tangency)
Answer by greenestamps(13203) (Show Source):
You can put this solution on YOUR website!

A radius of a circle to a point of tangency is perpendicular to the tangent at that point.

You are given a point of tangency (2,-7) and the equation of the tangent at that point. So you know the center of the circle is somewhere on the line that is perpendicular to the tangent at (2,-7); find the equation of that line.

You are also given the equation of another line that the center of the circle lies on.

You have equations for two lines that both contain the center of the circle. Solve the pair of equations to find the center of the circle.

Then use the distance formula to find the radius of the circle (distance between the center and (2,-7)).

Then plug the numbers into the standard form for the equation of a circle.