Let (x, y) be any point on the parabola y^2 = | vedclass

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

Question

(C) Let the coordinates of $P$ be $(h, k)$.Since $P$ divides the line segment joining $(0, 0)$ and $(x, y)$ in the ratio $1:3$,by the section formula,

Vedclass · Accepted Answer

$y^2 = x$

Vedclass · Answer

(C) Let the coordinates of $P$ be $(h, k)$.Since $P$ divides the line segment joining $(0, 0)$ and $(x, y)$ in the ratio $1:3$,by the section formula,the coordinates of $P$ are given by:$h = \frac{1 \cdot x + 3 \cdot 0}{1 + 3} = \frac{x}{4}$$k = \frac{1 \cdot y + 3 \cdot 0}{1 + 3} = \frac{y}{4}$Thus,$x = 4h$ and $y = 4k$.Since the point $(x, y)$ lies on the parabola $y^2 = 4x$,we substitute the values of $x$ and $y$:$(4k)^2 = 4(4h)$$16k^2 = 16h$$k^2 = h$Replacing $(h, k)$ with $(x, y)$,the locus of $P$ is $y^2 = x$.

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

Similar Questions

Find the equation of the parabola with focus $(4, -3)$ and vertex $(4, -1)$.

How many parabolas can be drawn if the two endpoints of the latus rectum are given?

If the chord joining the points $P_{1}(x_{1}, y_{1})$ and $P_{2}(x_{2}, y_{2})$ on the parabola $y^{2} = 12x$ subtends a right angle at the vertex of the parabola, then $x_{1}x_{2} - y_{1}y_{2}$ is equal to

The latus rectum of the conic passing through the origin and having the property that the normal at each point $(x, y)$ intersects the $x$-axis at $(x + 1, 0)$ is:

Let $A$ and $B$ be two distinct points on the parabola $y^{2}=4x$. If the axis of the parabola touches a circle of radius $r$ having $AB$ as its diameter, then the slope of the line $AB$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module