Conic Sections · JEE Preparation Mathematics

The equation of the tangent to the parabola y^2 = 16x at the point (4, 8) is:

Practice question from Conic Sections (JEE Preparation Mathematics), with the correct answer and a step-by-step solution.

hard · MCQ · Q-63EA0F

The equation of the tangent to the parabola y^2 = 16x at the point (4, 8) is:

  1. A.y = x + 4Correct answer
  2. B.y = 2x + 4
  3. C.y = x - 4
  4. D.y = 4x + 8

Solution

For y2=4axy^2=4ax, 4a=164a=16, so a=4a=4. The tangent at (x1,y1)=(4,8)(x_1,y_1)=(4,8) is yy1=2a(x+x1)yy_1=2a(x+x_1), giving 8y=8(x+4)8y=8(x+4) or y=x+4y=x+4.

More from Conic Sections

All of Conic Sections

Practise more Mathematics

Sign up free for adaptive practice on this chapter, with instant feedback and hints on every question.

Start practising free

Free to start · No credit card needed