Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

Let $\mathrm{O}$ be the vertex and $\mathrm{Q}$ be any point on the parabola $\mathrm{x^{2}=8y}$ , If the point $\mathrm{P}$ divides the line segment $\mathrm{OQ}$ internally in the ratio $\mathrm{1: 3}$ , then the locus of $\mathrm{P}$ is

Option: 1
$\mathrm{y^2=2 x}$

Option: 2
$\mathrm{x^2=2 y}$

Option: 3
$\mathrm{x^2=y}$

Option: 4
$\mathrm{y^2=x}$

Answers (1)

$\mathrm{O P: P Q=1: 3}$
Let the parametric co-ordinates of $\mathrm{Q\: be \: \left(4 t, 2 t^2\right)}$ We have, by section formula $\mathrm{\alpha=\frac{4 t+0}{4}=t\: and \: \beta=\frac{2 t^2+0}{4}=\frac{t^2}{2}}$ Eliminating $\mathrm{' t '}$ , we get the locus of $\mathrm{P(\alpha, \beta) \: as \: \alpha^2=2 \beta}$

Thus the locus is $\mathrm{x^2=2 y}$

Posted by

Kshitij

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

50 mL of 0.2 M ammonia solution is treated with 25 mL of 0.2 M HCl. If pK_b of ammonia solution is 4.75, the pH of the mixture will be :
Option: 1 3.75
Option: 2 4.75

Trending Articles/News

anam-khan

Amrita BTech Admission 2025: JEE Main-based registration deadline extended to August 30

anam-khan

DASA, CSAB Special round 2 seat allotment result 2025 declared on csab.nic.in

Latest Question