If the ellipse frac{x^{2}}{a^{2}}+frac{y^{2}} | vedclass

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

Question

(A) The ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ meets the line $\frac{x}{7}+\frac{y}{2\sqrt{6}}=1$ on the $x$-axis. Setting $y=0$ in the l

Vedclass · Accepted Answer

$\frac{5}{7}$

Vedclass · Answer

(A) The ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ meets the line $\frac{x}{7}+\frac{y}{2\sqrt{6}}=1$ on the $x$-axis. Setting $y=0$ in the line equation,we get $x=7$. Since the ellipse passes through $(7, 0)$,we have $a=7$.The ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ meets the line $\frac{x}{7}-\frac{y}{2\sqrt{6}}=1$ on the $y$-axis. Setting $x=0$ in the line equation,we get $y=-2\sqrt{6}$. Since the ellipse passes through $(0, -2\sqrt{6})$,we have $b^{2}=(-2\sqrt{6})^{2}=24$,so $b=2\sqrt{6}$.The eccentricity $e$ is given by $e^{2}=1-\frac{b^{2}}{a^{2}}$.Substituting the values,$e^{2}=1-\frac{24}{49} = \frac{25}{49}$.Therefore,$e=\frac{5}{7}$.

If the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ meets the line $\frac{x}{7}+\frac{y}{2\sqrt{6}}=1$ on the $x$-axis and the line $\frac{x}{7}-\frac{y}{2\sqrt{6}}=1$ on the $y$-axis,then the eccentricity of the ellipse is

Similar Questions

If the distance between the foci of an ellipse is $6$ and the length of the minor axis is $8$,then the eccentricity is

Given the base of a triangle and the sum of its other two sides,the locus of the center of its incircle is:

If the normal drawn at one end of the latus rectum of the ellipse $b^2 x^2 + a^2 y^2 = a^2 b^2$ with eccentricity $e$ passes through one end of the minor axis,then:

Find the number of real tangents that can be drawn from the point $(3, 5)$ to the ellipses $3x^2 + 5y^2 = 32$ and $25x^2 + 9y^2 = 450$.

Let the point $L$ lying in the first quadrant be one end of a latus rectum of the ellipse $\frac{x^2}{4}+\frac{y^2}{3}=1$. Let $P$ and $Q$ be the points where the normal drawn at $L$ to this given ellipse meets the major axis and the minor axis. Then the distance between $P$ and $Q$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module