Find the coordinates of the focus,axis of the parabola,the equation of the directrix,and the length of the latus rectum for $x^{2}=-9y$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The given equation is $x^{2}=-9y$.
Here,the coefficient of $y$ is negative.
Hence,the parabola opens downwards.
On comparing this equation with the standard form $x^{2}=-4ay$,we obtain:
$-4a = -9 \Rightarrow a = \frac{9}{4}$.
$\therefore$ The coordinates of the focus are $(0, -a) = (0, -\frac{9}{4})$.
Since the equation involves $x^{2}$,the axis of the parabola is the $y$-axis.
The equation of the directrix is $y = a$,i.e.,$y = \frac{9}{4}$.
The length of the latus rectum is $4a = 9$.

Explore More

Similar Questions

Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$,focus $(-2, 0)$.

For the parabola $y=x^2-3x+2$,match the items in List-$I$ to that of the items in List-$II$. $S$ is a focus,$Z$ is the intersection of the axis and the directrix,$P$ is one end point of the latus rectum,$Q$ is the point on the parabola at which the tangent is parallel to the $X$-axis.
$A$. $P$$I$. $(2,0)$
$B$. $Q$$II$. $(\frac{3}{2}, -\frac{1}{4})$
$C$. $S$$III$. $(\frac{3}{2}, 0)$
$D$. $Z$$IV$. $(\frac{3}{2}, -\frac{1}{2})$
$V$. $(0, \frac{3}{2})$

If the normal drawn at $P(8, 16)$ to the parabola $y^2 = 32x$ meets the parabola again at $Q$,then the equation of the tangent drawn at $Q$ to the parabola is

If the line $3x - 2y + 12 = 0$ intersects the parabola $4y = 3x^2$ at the points $A$ and $B$,then at the vertex of the parabola,the line segment $AB$ subtends an angle equal to

Find the equation of the parabola whose axis is parallel to the $y$-axis and which passes through the points $(0,4), (1,9)$ and $(4,5)$.

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