Question

What are the x- and y-intercepts of the line tangent to the circle (x – 2)2 + (y – 2)2 = 52 at the point (5, 6)?

Answer 1

1 ) They are perpendicular.
2 ) m · (-1) / m = -1.
The product of the slopes is -1.
3 ) The center of the circle is ( 2, 2 ).
4 ) m = (6-2 ) / 5 -2 = 4/3
5 ) Slope of the tangent: m = - 3/4.
6 ) m = -3/4, passes through the point: ( 5. 6 ):
6 = - 15/4 + b
b = 24/4 + 15/4
b = 39/4
The slope-intercept equation is:
y = -3/4 x + 39/4
7) We will put : x = 0 in the linear equation.
8 ) We will put y = 0 in the linear equation.
9 ) y-intercept : y = 9.75
Zero: x = 13.