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TS EAMCET · Maths · Parabola

If the line \(y=-x+k\) is normal to the curve \(y^2=16 x\), then \(k\) is

  1. A 21
  2. B 14
  3. C 13
  4. D 12
Verified Solution

Answer & Solution

Correct Answer

(D) 12

Step-by-step Solution

Detailed explanation

Normal of the parabola \(y^2=16 x\) is \[ y=m x-8 m-4 m^3 \] Now, \(y=-x+k\) is normal of parabola \[ \therefore \quad m=-1 \] put \(m=-1\) in Eq. (i) we get \[ \begin{aligned} y & =-x+8+4 \\ y & =-x+12 \\ \therefore \quad k & =12 \end{aligned} \]