Question

find the equation of the tangent line to the circle x^2+y^2=25

Answer 1

Since no particular point is given we can take as general point (x1,y1)

For finding slope of tangent , we find derivative.

Differentiate the equation with respect to x

2x + 2y y' = 0

Or slope = -x1/y1

Using point slope formula

equation of tangent passing through (x1,y1) and having slope (-x1/y$y-y1 = \frac{-x1}{y1} (x-x1)</p><p>xx1+yy1 = x1^2+y1^2 = 25$1) is

So answer is xx1+yy1 = 25