(B) Let $x = (u \cos \alpha)t$ and $y = (u \sin \alpha)t - \frac{1}{2}gt^2$.From the first equation,we have $t = \frac{x}{u \cos \alpha}$.Substituting

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

(B) Let $x = (u \cos \alpha)t$ and $y = (u \sin \alpha)t - \frac{1}{2}gt^2$.From the first equation,we have $t = \frac{x}{u \cos \alpha}$.Substituting this value of $t$ into the equation for $y$:$y = (u \sin \alpha) \left( \frac{x}{u \cos \alpha} \right) - \frac{1}{2}g \left( \frac{x}{u \cos \alpha} \right)^2$$y = x \tan \alpha - \frac{g x^2}{2 u^2 \cos^2 \alpha}$.This equation is of the form $y = ax^2 + bx + c$,which represents a parabola.

Class 11 Mathematics 10-2. Parabola, Ellipse, Hyperbola Parabola

Medium

The position of a moving point in the $XY$-plane at time $t$ is given by $\left( (u \cos \alpha)t, (u \sin \alpha)t - \frac{1}{2}gt^2 \right)$,where $u, \alpha, g$ are constants. The locus of the moving point is

A
$A$ circle
B
$A$ parabola
C
An ellipse
D
None of these

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

10-2. Parabola, Ellipse, Hyperbola

Subtopic

Parabola

If the ordinates of points $P$ and $Q$ on the parabola $y^2=12x$ are in the ratio $1:2$,then the locus of the point of intersection of the normals to the parabola at $P$ and $Q$ is

MediumAP EAMCET 2024

View Solution

If the focal chord drawn through the point $P(5,5)$ to the parabola $y^2=5x$ meets the parabola again at the point $Q$,then the tangent drawn to this parabola at $Q$ meets the axis of the parabola at the point

EasyAP EAMCET 2023

View Solution

Find the length of the chord of the parabola $y^2 = 4ax$ which passes through the vertex and makes an angle $\theta$ with the $x-$axis.

Difficult

View Solution

If two parabolas $y^2 = 4x$ and $x^2 = 32y$ intersect at the point $(16, 8)$ at an angle $\theta$,then what is the value of $\tan \theta$?

Difficult

View Solution

If $b$ and $c$ are the lengths of the segments of any focal chord of a parabola $y^2 = 4ax$,then the length of the semi-latus rectum is:

MediumTS EAMCET 2006

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The position of a moving point in the $XY$-plane at time $t$ is given by $\left( (u \cos \alpha)t, (u \sin \alpha)t - \frac{1}{2}gt^2 \right)$,where $u, \alpha, g$ are constants. The locus of the moving point is

Similar Questions

If the ordinates of points $P$ and $Q$ on the parabola $y^2=12x$ are in the ratio $1:2$,then the locus of the point of intersection of the normals to the parabola at $P$ and $Q$ is

If the focal chord drawn through the point $P(5,5)$ to the parabola $y^2=5x$ meets the parabola again at the point $Q$,then the tangent drawn to this parabola at $Q$ meets the axis of the parabola at the point

Find the length of the chord of the parabola $y^2 = 4ax$ which passes through the vertex and makes an angle $\theta$ with the $x-$axis.

If two parabolas $y^2 = 4x$ and $x^2 = 32y$ intersect at the point $(16, 8)$ at an angle $\theta$,then what is the value of $\tan \theta$?

If $b$ and $c$ are the lengths of the segments of any focal chord of a parabola $y^2 = 4ax$,then the length of the semi-latus rectum is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module