Let P be the mid-point of a chord joining the | vedclass

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

Question

(B) The vertex of the parabola $y^{2}=8x$ is $M(0,0)$.Let the other point on the parabola be $N(2t^{2}, 4t)$, where $t$ is a parameter.Let $P(x, y)$ b

Vedclass · Accepted Answer

$y^{2}=4x$

Vedclass · Answer

(B) The vertex of the parabola $y^{2}=8x$ is $M(0,0)$.Let the other point on the parabola be $N(2t^{2}, 4t)$, where $t$ is a parameter.Let $P(x, y)$ be the mid-point of the chord $MN$.Using the mid-point formula, we have:$x = \frac{0 + 2t^{2}}{2} = t^{2}$$y = \frac{0 + 4t}{2} = 2t$From the second equation, $t = \frac{y}{2}$.Substituting this into the first equation:$x = (\frac{y}{2})^{2}$$x = \frac{y^{2}}{4}$$y^{2} = 4x$Thus, the locus of $P$ is $y^{2}=4x$.

Let $P$ be the mid-point of a chord joining the vertex of the parabola $y^{2}=8x$ to another point on it. Then, the locus of $P$ is

Similar Questions

The equation of a tangent to the parabola $y^2 = 8x$ is $y = x + 2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

Let $L$ be a normal to the parabola $y^2=4x$. If $L$ passes through the point $(9,6)$,then $L$ is given by
$(A)$ $y-x+3=0$ $(B)$ $y+3x-33=0$ $(C)$ $y+x-15=0$ $(D)$ $y-2x+12=0$

If the focus of a parabola is $(3, 0)$ and the length of its latus rectum is $8$,what is its vertex?

The length of the latus rectum of the parabola $4y^2 + 2x - 20y + 17 = 0$ is

The equation of the directrix of the parabola ${x^2} + 8y - 2x = 7$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module