If the line x + y = 1 is a normal to the para | vedclass

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

Question

(B) The equation of the line is $y = -x + 1$,which is in the form $y = mx + c$,where $m = -1$ and $c = 1$. For a parabola $y^2 = 4ax$,the condition fo

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) The equation of the line is $y = -x + 1$,which is in the form $y = mx + c$,where $m = -1$ and $c = 1$. For a parabola $y^2 = 4ax$,the condition for the line $y = mx + c$ to be a normal is $c = -2am - am^3$. Comparing $y^2 = kx$ with $y^2 = 4ax$,we get $4a = k$,so $a = k/4$. Substituting $m = -1$ and $c = 1$ into the condition: $1 = -2(k/4)(-1) - (k/4)(-1)^3$ $1 = (k/2) + (k/4)$ $1 = (2k + k) / 4$ $1 = 3k / 4$ $k = 4/3$.

If the line $x + y = 1$ is a normal to the parabola $y^2 = kx$,then find the value of $k$. (in $/3$)

Similar Questions

Find the equation of the parabola with vertex at $(0, 1)$ and focus at $(0, 0)$.

From the point $(-1, 2)$,tangent lines are drawn to the parabola $y^2 = 4x$. Find the equation of the chord of contact.

Let $(x, y)$ be any point on the parabola $y^2 = 4x$. Let $P$ be a point that divides the line segment from $(0, 0)$ to $(x, y)$ in the ratio $1 : 3$. Find the locus of $P$.

The equation of the directrix of the parabola $y^2-x+4y+5=0$ is

Let the locus of the mid-point of the chord through the origin $O$ of the parabola $y^{2}=4x$ be the curve $S$. Let $P$ be any point on $S$. Then the locus of the point, which internally divides $OP$ in the ratio $3:1$, is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module