Let the lines l_1 and l_2 be normals to y^2=4x and tangents to x^2=-12y (where l_1 and l_2 are not x-axis). The absolute value of the difference of…

Question

Let the lines l_1 and l_2 be normals to y^2=4x and tangents to x^2=-12y (where l_1 and l_2 are not x-axis). The absolute value of the difference of slopes of l_1 and l_2 is

MARKS Content Team · Accepted Answer

Correct answer: (C) 1. The tangent to x^2=-12y is kx=y+-3k^2 Normal to y^2=4x is y=mx-2m-m^3 ⇒k=m & 2m+m^3=-3k^2 ⇒mm^2+3m+2=0⇒m=-1,-2 ( m=0 is rejected) Hence, the difference of slopes is equal to 1

Let the lines $l_{1}$ and $l_{2}$ be normals to $y^{2} = 4 x$ and tangents to $x^{2} = - 12 y$ (where $l_{1}$ and $l_{2}$ are not $x$ -axis). The absolute value of the difference of slopes of $l_{1}$ and $l_{2}$ is

Solution

More Parabola Questions

Let the lines l1 and l2 be normals to y2=4x and tangents to x2=-12y (where l1 and l2 are not x-axis). The absolute value of the difference of slopes of l1 and l2 is

Solution

More Parabola Questions

Let the lines $l_{1}$ and $l_{2}$ be normals to $y^{2} = 4 x$ and tangents to $x^{2} = - 12 y$ (where $l_{1}$ and $l_{2}$ are not $x$ -axis). The absolute value of the difference of slopes of $l_{1}$ and $l_{2}$ is