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)?

Refresh if you see errors.the x-intercept is 13.the y-intercept is 39/4, or 9.75======to find the x- and y-intercepts of the line tangent to that circle, we need the equation of the tangent line.to get the equation of the tangent line, we need the slope of that tangent line.to find the slope of that tangent line to the circle, we need a derivative expression for the circle.to get the derivative expression, we need to implicitly differentiate the equation of the circle. differentiate both sides of the equation, treating y as a function of x.    using chain rule, we have      and    so using these in our original equation, we solve for :     so the slope of the tangent line to this circle at (5,6) is    and the equation of this tangent line, using point-slope form, is    ======to find x-intercept, the x-intercept occurs when y=0. set y=0 and solve for x.    the x-intercept is 13.to find y-intercept, the y-intercept occurs when x=0.set x=0 and solve for y.    the y-intercept is  39/4, or 9.75.