Find the general equation of the circle.

Question

If the circle is tangent to the line -3x+2y+1=0 at the point (1, 1), and the center is on the line x+y-1=0.

Answer 1

I will not do this problem for you, but I will tell you how to do it.

Draw a sketch!

From the equation of the tangent the slope of the tangent is 3/2.

The normal at (1,1) will have slope -2/3.

Use the point slope form to get the equation of the normal.

The center of the circle will be at the intersection of the normal and the given line, i.e. solve the two linear equations; the solution will be the co-ordinates of the center.

Then use the distance formula to calculate the distance from the center to (1,1); that is the radius of the circle.

The equation of a circle with radius r and center (h,k) is (x-h)² + (y-k)² = r².