The angle between the lines joining the foci | vedclass

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

Question

(D) Let the ellipse be $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. The foci are $S(ae, 0)$ and $S'(-ae, 0)$, and the extremity of the minor axis is $B(0,

Vedclass · Accepted Answer

$\frac{1}{\sqrt{2}}$

Vedclass · Answer

(D) Let the ellipse be $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. The foci are $S(ae, 0)$ and $S'(-ae, 0)$, and the extremity of the minor axis is $B(0, b)$.Given that the angle $\angle SBS' = 90^{\circ}$.Since the triangle $	riangle SBS'$ is isosceles with $SB = S'B$, the altitude from $B$ to $SS'$ bisects the angle $\angle SBS'$.Thus, $\angle OBS = 45^{\circ}$.In the right-angled triangle $	riangle OBS$, we have $	an(45^{\circ}) = \frac{OB}{OS} = \frac{b}{ae}$.Since $	an(45^{\circ}) = 1$, we get $1 = \frac{b}{ae}$, which implies $b = ae$.Using the relation $b^2 = a^2(1 - e^2)$, we substitute $b^2 = a^2e^2$:$a^2e^2 = a^2(1 - e^2)$$e^2 = 1 - e^2$$2e^2 = 1$$e^2 = \frac{1}{2}$$e = \frac{1}{\sqrt{2}}$.

The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is $90^{\circ}$. The eccentricity of the ellipse is

Similar Questions

An ellipse is drawn such that the diameter of the circle $(x - 1)^2 + y^2 = 1$ is the semi-minor axis and the diameter of the circle $x^2 + (y - 2)^2 = 4$ is the semi-major axis. If the center of the ellipse is at the origin and its axes are the coordinate axes,find the equation of the ellipse.

The line $y=x+1$ meets the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{2}=1$ at two points $P$ and $Q$. If $r$ is the radius of the circle with $PQ$ as diameter,then $(3r)^{2}$ is equal to

Find the equation of the ellipse whose major axis is $8$ and eccentricity is $1/2$ $(a > b)$.

An ellipse with its minor and major axes parallel to the coordinate axes passes through $(0,0)$,$(1,0)$,and $(0,2)$. One of its foci lies on the $Y$-axis. The eccentricity of the ellipse is

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module