Find the equation of the tangent line to the circle with center at the origin, at point (9,7). Write the answer in general form.

Question

Thank you.

Answer 1

The general equation is x²+y²=a² where a is the radius. The point lies on the circle, so a²=9²+7²=81+49=130, and the equation x²+y²=130. The tangent is found by differentiating this equation:

x+ydy/dx=0, dy/dx=-x/y=-9/7.

Equation of the tangent is y-7=-9(x-9)/7, y=-9x/7+81/7+7=-9x/7+130/7 or y=(-9x+130)/7.