Show that the tangent lines to the curve y2= 4 ax at the point x= a are orthogonal.
Dear Student,
y2 = 4ax
When x = a
y2 = 4a2
=> y = +2a
points are (a, 2a) and (a, - 2a)
Slope of the tangent of the curve y2 = 4ax is
y dy/dx = 4a
dy/dx = 2a/y
for y = 2a, dy/dx = 1 = m1
for y = -2a dy/dx = - 1 = m2
m1m2 = -1
Regards