How To: Find the equation of a circle given: center & tangent

Find the equation of a circle given: center & tangent

In this video, the instructor shows how to find the equation of a circle given its center point and a tangent line to it. To do this, take a graph and plot the given point and the tangent on that graph. Now, from the center of the circle, measure the perpendicular distance to the tangent line. This gives us the radius of the circle. Using the center point and the radius, you can find the equation of the circle using the general circle formula (x-h)*(x-h) + (y-k)*(y-k) = r*r, where (h,k) is the center of your circle and r is the radius. Now substitute these values in that equation. Expand the equation and sum up the common terms by bringing all the terms to the left side. This gives the equation of the circle.

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