equation of a tangent line

Question

write the equation of the line that is tangent to x^2+y^2=100; (8,6)

Answer 1

A line tangent to a circle and radius to the point of tangency are perpendicular.

The radius with end point (8,6) has slope = (6-0)/(8-0) = 6/8 = 3/4

So the slope of the tangent line is reciprocal to (8,6) is -4/3.

An equation to the tangent line follows

Point slope form y-6 = -4/3(x-8)

Cross multiplication.

3y-18 = -4x+32

Add 18 to each side.

3y = -4x+50

Divide to each side by 3.

y = (-4/3)x+50/3