Question

What are the x- and y-intercepts of the line tangent to the circle (x – 2)2 + (y – 2)2 = 25 at the point (5, 6)?

Answer 1

I'm assuming you have. The first thing we do is find the slope of the tangent line by finding the derivative of the equation at the point (5,6).

expanding the equation

x^2 - 4x + 4 + y^2 - 4y + 4 = 25

Finding the derivative

2x - 4 + 2y y' - 4y' = 0

y'( 2y - 4) = 4 - 2x

y' = (4 - 2x) / (2y - 4)

at the point (5,6) the slope = y' = (4 - 10) / (12 - 4) = -3/4

So the equation of tangent line is y - 6 = -3/4( x - 5)

y = -3/4x + 39/4

so the y intercept = =3/4(0) + 39/4 = 39/4 Answer

and x intercept = -39/4 / - 3/4 = 13 Answer