+47 A circle’s equation is represented by (x - 4)2 + (y + 1)2 = 25. Find the equation of the two tangent lines that have slopes of -¾.
+128474 (x - 4)^2 + (y + 1)^2 = 25
The center of this circle is ( 4, -1)
We can use the negative reciprocal slope to -3/4 =4/3 to find the points where the tangent lines touch the circle
If we move 3 units to the right on x and 4 units up on y from the center we will have the first point where a tangent line touches this circle = ( 7, 3)
Likewise....if we move 3 units to the left and 4 units down from the center we will have the second point where a tangent line touches the circle = ( 1, -5)
The equation of the first line is
y = (-3/4)(x - 7) + 3
The equation of the second line is
y =(-3/4)(x - 1) -5
See the graph here : https://www.desmos.com/calculator/mztyclw9nw
