Question

 Find the equation of the normal to the parabola y² = 4x which is parallel to y – 2x + 5 = 0. 

Answer 1

Given the parabola is y² = 4x 

∴ a = 1 

 Given line y – 2x + 5 = 0 

 Slope m = 2 

The normal is parallel to the line y – 2x+5 = 0 

 Slope of the normal = 2 

Equation of the normal at ‘t’ is y + tx = 2at + at³ 

∴ Slope = –t = 2 (⇒t = –2) 

Equation of the normal is y-2x =2.1(-2) +1( -2)³-4 -8 = -12 

 2x – y – 12 = 0.