Let l_1 and l_2 be the two lines which are normal to y^2=4x and tangent to x^2=-12y respectively (where, l_1 and l_2 are not the x-axis). Then, the…

Question

Let l_1 and l_2 be the two lines which are normal to y^2=4x and tangent to x^2=-12y respectively (where, l_1 and l_2 are not the x-axis). Then, the product of the slopes of l_1 and l_2 is

MARKS Content Team · Accepted Answer

Correct answer: (B) 2. Let the slope of the tangent be k, then the equation of the tangent to x^2=-12y is kx=y+-3k^2 Let the slope of the normal be m, then the equation of the normal to y^2=4x is y=mx-2m-m^3 ⇒k=m and 2m+m^3=-3k^2 ⇒mm^2+3m+2=0⇒m=-1,-2 (m=0 is rejected)

Let $l_{1}$ and $l_{2}$ be the two lines which are normal to $y^{2} = 4 x$ and tangent to $x^{2} = - 12 y$ respectively (where, $l_{1}$ and $l_{2}$ are not the $x$ -axis). Then, the product of the slopes of $l_{1}$ and $l_{2}$ is

Solution

More Parabola Questions

Let l1 and l2 be the two lines which are normal to y2=4x and tangent to x2=-12y respectively (where, l1 and l2 are not the x-axis). Then, the product of the slopes of l1 and l2 is

Solution

More Parabola Questions

Let $l_{1}$ and $l_{2}$ be the two lines which are normal to $y^{2} = 4 x$ and tangent to $x^{2} = - 12 y$ respectively (where, $l_{1}$ and $l_{2}$ are not the $x$ -axis). Then, the product of the slopes of $l_{1}$ and $l_{2}$ is