Equation of circle given center and tangent line

Question

Write the equation for a circle which has its center at (1, 2) and is tangent to the line -3x+2y= 14 Solve algebraically.

 

I know that the equation of a circle is r²=(x-h)²+(y-k)². So, at this point the equation is r²=(x-1)²+(y-2)². I also can rearrange the tangent line equation to get y=(3/2)x+7. I was wondering if I can just substitute (3/2)x+7 for y in the equation of the circle. If I can't, what should I do? If I can, is there a better way to do this? Thanks. 

Answer 1

You can find the radius in the following way. 

Write the equation of the line that is perpendicular to the given tangent line. This perpendicular goes through the stated center, and intersects the tangent; the perpendicular's slope is the negative reciprocal of the stated tangent line.

Find the intersection (point T) of the tangent and radius line--then use the distance formula to find the radius, which is a segment from the stated center to the point T.