Find the equation of the chord of the parabola y 2 = 12x which is bisected at the point (5, –7)

Dear student,

let (x1,y1) and (x2,y2) be two point be on parabola and (5,-7) is their midpoint

=> x1+x2 = 10 , y1+y2 = -14

yi^2 = 12xi

=> y1^2 + y2^2 = 120 and y1+y2 = -14

=> y1+y2)^2 = 196

=> 120 + 2y1y2 = 196

=> y1y2 = 38 => y2 = 38/y1

substitute it in y1+y2 = -14

=> y1^2 + 14y1 + 38 = 0

=> y1 = -3.68 , x1 = 1.13 and y2 = 10.316 , x2 = 8.869

line passing through (x1,y1) and (x2,y2) is y= (-6/7)x + (-19/7)