(A) The slope of the tangent $m = \tan(45^{\circ}) = 1$. For the parabola $y^2 = 4Ax$,the slope of the tangent at point $(At^2, 2At)$ is $m = 1/t$. Co

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

$\left( \frac{a}{4}, \frac{a}{2} \right)$

(A) The slope of the tangent $m = \tan(45^{\circ}) = 1$. For the parabola $y^2 = 4Ax$,the slope of the tangent at point $(At^2, 2At)$ is $m = 1/t$. Comparing $y^2 = ax$ with $y^2 = 4Ax$,we get $4A = a$,so $A = a/4$. Since $m = 1/t = 1$,we have $t = 1$. The point of contact is $(At^2, 2At) = (\frac{a}{4}(1)^2, 2(\frac{a}{4})(1)) = (\frac{a}{4}, \frac{a}{2})$.

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

Medium

If the tangent to the parabola $y^2 = ax$ makes an angle of $45^{\circ}$ with the $x$-axis,what is its point of contact?

A
$\left( \frac{a}{4}, \frac{a}{2} \right)$
B
$\left( \frac{a}{2}, \frac{a}{2} \right)$
C
$\left( -\frac{a}{2}, \frac{a}{4} \right)$
D
$\left( -\frac{a}{4}, \frac{a}{2} \right)$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

10-2. Parabola, Ellipse, Hyperbola

Subtopic

Parabola

Find the equation of the latus rectum of the parabola $x^2 = -12y$.

Easy

View Solution

The vertices of the base of an isosceles triangle lie on a parabola $y^2=4x$ and the base is a part of the line $y=2x-4$. If the third vertex of the triangle lies on the $X$-axis,its coordinates are

KVPY 2013

View Solution

The tangents at the points $A(1, 3)$ and $B(1, -1)$ on the parabola $y^{2} - 2x - 2y = 1$ meet at the point $P$. Then the area (in unit$^{2}$) of the triangle $PAB$ is:

DifficultJEE MAIN 2022

View Solution

Let the equation of the tangent at a point $P$ on the parabola $x^2-4x-4y+16=0$ be $2x-y-5=0$. If the equation of the normal drawn at $P$ to this parabola is $ax+y+c=0$,then find the value of $ac$.

MediumAP EAMCET 2023

View Solution

Find the locus of the midpoints of all focal chords of the parabola $y^2 = 4ax$.

Difficult

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

If the tangent to the parabola $y^2 = ax$ makes an angle of $45^{\circ}$ with the $x$-axis,what is its point of contact?

Similar Questions

Find the equation of the latus rectum of the parabola $x^2 = -12y$.

The vertices of the base of an isosceles triangle lie on a parabola $y^2=4x$ and the base is a part of the line $y=2x-4$. If the third vertex of the triangle lies on the $X$-axis,its coordinates are

The tangents at the points $A(1, 3)$ and $B(1, -1)$ on the parabola $y^{2} - 2x - 2y = 1$ meet at the point $P$. Then the area (in unit$^{2}$) of the triangle $PAB$ is:

Let the equation of the tangent at a point $P$ on the parabola $x^2-4x-4y+16=0$ be $2x-y-5=0$. If the equation of the normal drawn at $P$ to this parabola is $ax+y+c=0$,then find the value of $ac$.

Find the locus of the midpoints of all focal chords of the parabola $y^2 = 4ax$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module