This is on secant of the circle. The line intersects the circle, find the coordinates of each point of intersection. L:5y+3x=25 C: x2+y2-4x+6y-21=0
+129840 L:5y+3x=25 → y = [25 -3x] / 5 (1)
C: x^2+y^2-4x+6y-21=0 (2) put (1) into (2)
x^2 + ( [25 -3x] / 5)^2 - 4x + 6 [25 -3x] / 5 - 21 = 0
x^2 + [ 625 - 150x + 9x^2] / 25 - 4x + (6/5) [25 -3x] - 21 = 0
Multiply by 25
25x^2 + 625 - 150x + 9x^2 - 100x + 30 [25 -3x] - 525 = 0
34x^2 - 250x + 625 + 750 - 90x - 525 = 0
34x^2 - 340x + 850 = 0 divide by 2
17x^2 - 170x + 425 = 0 divide by 17
x^2 - 10x + 25 = 0 factor
(x - 5)^2 = 0 → x = 5 and y = [25 -3x] / 5 = [25 -3(5)] / 5 = 2
So...the intersection is at (5,2)
Graph :
P.S. - This is a tangent, not a secant.....
