SOLUTION: The circle is tangent to the line 4x+3y=4 at the point (4,-4) and center is on the line x-y=7. Find the equation of the circle. (I'm struggling to find the center in x-y=7 that say

Question 1139514: The circle is tangent to the line 4x+3y=4 at the point (4,-4) and center is on the line x-y=7. Find the equation of the circle. (I'm struggling to find the center in x-y=7 that says to be perpendicular to the center itself and to the point of tangency)
Answer by greenestamps(13208) (Show Source): You can put this solution on YOUR website!

Put the equations in slope-intercept form.

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If the circle is tangent to the line at (4,-4), then the center of the circle has to lie on the line with slope 3/4 passing through (4,-4). (A radius to a point of tangency is perpendicular to the tangent; slopes of perpendicular lines are negative reciprocals.)

So the center of the circle lies on the line .

The given information says that the center of the circle lies on the line .

So the center of the circle is at the one point that lies on both and .

Solve that pair of equations to find the intersection point; that is the center of the circle.
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