If the line x + y = k is a normal to the para | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The equation of the parabola is $y^2 = 4ax$,where $4a = 4$,so $a = 1$.The equation of a normal to the parabola $y^2 = 4ax$ at point $(at^2, 2at)$

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) The equation of the parabola is $y^2 = 4ax$,where $4a = 4$,so $a = 1$.The equation of a normal to the parabola $y^2 = 4ax$ at point $(at^2, 2at)$ is $y = -tx + 2at + at^3$.Given the line is $x + y = k$,which can be written as $y = -x + k$.Comparing $y = -x + k$ with $y = -tx + 2at + at^3$,we get $t = 1$.Substituting $t = 1$ and $a = 1$ into the expression for $k$:$k = 2at + at^3 = 2(1)(1) + 1(1)^3 = 2 + 1 = 3$.Therefore,the value of $k$ is $3$.

If the line $x + y = k$ is a normal to the parabola $y^2 = 4x$,find the value of $k$.

Similar Questions

An equilateral triangle is inscribed in the parabola $y^{2}=4ax$,where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

Find the angle $\alpha$ between the tangents drawn from the point $(-2, -1)$ to the parabola $y^2 = 4x$. What is the value of $\tan \alpha$?

From a point $(C, 0)$,three normals are drawn to the parabola $y^2=x$. Then,

$A$ point on the parabola whose focus is $S(1,-1)$ and whose vertex is $A(1,1)$ is

If the vertex and focus of a parabola lying on the $x$-axis are at distances $p$ and $q$ from the origin respectively,find its equation.

Vedclass Test Series

Exam Paper Generator

Online Exam Module