Find the equation for the ellipse that satisf | vedclass

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

Question

(A) The vertices are given as $(0, \pm 13)$,which lie on the $y$-axis. Thus,the major axis is along the $y$-axis,and the equation of the ellipse is of

Vedclass · Accepted Answer

$\frac{x^{2}}{144} + \frac{y^{2}}{169} = 1$

Vedclass · Answer

(A) The vertices are given as $(0, \pm 13)$,which lie on the $y$-axis. Thus,the major axis is along the $y$-axis,and the equation of the ellipse is of the form $\frac{x^{2}}{b^{2}} + \frac{y^{2}}{a^{2}} = 1$. Here,$a = 13$ and the foci are $(0, \pm c)$ where $c = 5$. Using the relation $a^{2} = b^{2} + c^{2}$,we have $13^{2} = b^{2} + 5^{2}$. $169 = b^{2} + 25$. $b^{2} = 169 - 25 = 144$. Substituting the values of $a^{2}$ and $b^{2}$ into the standard equation,we get $\frac{x^{2}}{144} + \frac{y^{2}}{169} = 1$.

Find the equation for the ellipse that satisfies the given conditions: Vertices $(0, \pm 13)$,foci $(0, \pm 5)$.

Similar Questions

Tangents are drawn to the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{5}=1$ at the ends of both latus recta. The area of the quadrilateral so formed is

If the focal distance of an endpoint of the minor axis of an ellipse (taking its axes as the $x$ and $y$ axes respectively) is $k$ and the distance between its foci is $2h$,then its equation is:

$S$ and $T$ are the foci of an ellipse and $B$ is the end point of the minor axis. If $\triangle STB$ is an equilateral triangle, the eccentricity of the ellipse is

$A$ tangent drawn at a point on the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ cuts the $X$-axis at point $A$. If $A^{\prime}$ is the image of $A$ with respect to the line $y=x$,then the circle with $AA^{\prime}$ as its diameter passes through the fixed point:

Find the coordinates of the foci,the vertices,the length of the major axis,the minor axis,the eccentricity,and the length of the latus rectum of the ellipse $\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module