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)? pleasw

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

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step-by-step explanation:

can i see a photo of the question so i can you?