Asked by Anonymous

Find an equation for the line tangent to the circle x^2 + y^2 = 25 at the point (3, -4),
Answered by mathhelper
Step1 would be to make sure the given point actually lies on the line.
Suppose the given point had been given as (1,6). I could repeat the
following steps and get a totally meaningless result, even know nothing
unbecoming would show up in my solution.
Yes, the point does lie on the circle, so .....

Differentiate implicitly,
x^2 + y^2 = 25
2x + 2y dy/dx = 0
dy/dx = -x/y
so at (3, -4) , dy/dx = slope = -3/-4 = 3/4

equation of tangent:
y + 4 = (3/4)(x - 3)
4y + 16 = 3x - 9
3x - 4y = 25

Can you see a pattern here?
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