Find the coordinates of the focus,axis of the parabola,the equation of the directrix,and the length of the latus rectum for $x^{2}=6y$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The given equation is $x^{2}=6y$.
Comparing this with the standard form $x^{2}=4ay$,we get $4a=6$,which implies $a=\frac{3}{2}$.
Since the coefficient of $y$ is positive,the parabola opens upwards.
$1$. Coordinates of the focus: $(0, a) = (0, \frac{3}{2})$.
$2$. Axis of the parabola: Since the equation involves $x^{2}$,the axis is the $y$-axis $(x=0)$.
$3$. Equation of the directrix: $y = -a$,so $y = -\frac{3}{2}$.
$4$. Length of the latus rectum: $4a = 6$.

Explore More

Similar Questions

The length of the latus rectum of the parabola $y^2 - 4y - 2x - 8 = 0$ is:

If the line $2x + y + k = 0$ is normal to the parabola $y^2 = -8x$,then the value of $k$ will be

The equations of the normals at the ends of the latus rectum of the parabola $y^{2}=4ax$ are given by

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

Which of the following represents a parabola?

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