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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Parabola

NTA Abhyas 2020 · Mathematics · Parabola

Let the lines l _ 1 and l _ 2 be normals to y^ 2 = 4x and tangents...

Let the lines l1{l}_{1} and l2{l}_{2} be normals to y2=4xy^{2} = 4x and tangents to x2=−12yx^{2} = - 12y (where l1{l}_{1} and l2{l}_{2} are not xx-axis). The absolute value of the difference of slopes of l1{l}_{1} and l2{l}_{2} is

Options

  1. A33
  2. B22
  3. C11
  4. D12\dfrac{1}{2}

Correct answer

C. 11

Step-by-step solution

The tangent to x2=−12yx^{2} = - 12y is kx=y+(−3)k2kx = y + \left(- 3\right)k^{2}
Normal to y2=4xy^{2} = 4x is y=mx−2m−m3y = mx - 2m - m^{3}
⇒k=m and 2m+m3=−3k2⇒ k = m \text{ and } 2m + m^{3} = - 3k^{2}
⇒m(m2+3m+2)=0⇒m=−1,−2⇒ m\left(m^{2} + 3m + 2\right) = 0 ⇒ m = - 1, - 2 (m = 0isrejected)<br/>Hence,thedifferenceofslopesisequalto1is rejected)<br />Hence, the difference of slopes is equal to 1
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