Find the equation of chord of parabola
y2 = 4x whose midpoint is (4, 2)
x−y−2=0
Equation of the chord of the parabola y2 = 4ax whose middle point is (x1 , y1) is
T = S1
yy1 − 2a(x+x1) = y21 − 4ax1
yy1 − y21 = 2ax + 2ax1 − 4ax1
y1(y − y1) = 2a(x − x1)
y − y1 = 2ay1(x − x1)
substituting ,x1 = 4,y1 = 2 and a = 1
y − 2 = 22(x − 4)
y − 2 = x − 4
x − y − 2 = 0