Ellipse

What is the eccentricity of the ellipse if the angle between the straight lines joining the foci to an extremity of the minor axis is $90^{\circ}$ ?

What is the equation of the ellipse whose vertices are $(\pm 5,0)$ and foci are at $(\pm 4,0)$ ?

Consider any point P on the ellipse $\frac{\mathrm{x}^2}{25}+\frac{\mathrm{y}^2}{9}=1$ in the first quadrant. Let $r$ and $s$ represent its distances from $(4,0)$ and $(-4,0)$ respectively, then $(r+s)$ is equal to

If the angle between the lines joining the end points of minor axis of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with one of its foci is $\frac{\pi}{2}$, then what is the eccentricity of the ellipse?

The equation of the ellipse whose vertices are at $(\pm 5,0)$ and foci at $(\pm 4,0)$ is

A man running round a racecourse notes that the sum of the distances of two flag-posts from him is always 10 m and the distance between the flag-posts is 8 m . The area of the path he encloses is

Let $P(x, y)$ be any point on the ellipse $25 x^2+16 y^2=400$. If $Q(0,3)$ and $R(0,-3)$ are two points, then what is $(P Q+P R)$ equal to?

Passage: The foci of the ellipse $px^2+16y^2=16p$ and the foci of the hyperbola $25(81x^2-144y^2)=11664$ coincide (assume $pQuestion: What is the difference between the eccentricities of the hyperbola and the ellipse ?$

If any point on an ellipse is $(3\sin\alpha, 5\cos\alpha)$, then what is the eccentricity of the ellipse?

Paragraph: Consider the following for the next two $(02)$ items that follow: $\mathrm{P}(x, y)$ is any point on the ellipse $x^2+4 y^2=1$. Let $E, F$ be the foci of the ellipse. Question: Consider the following points:…

Given that $4 x^2+y^2=9$ What is the maximum value of y?

Consider the following in respect of the equation $\frac{x^2}{24-k}+\frac{y^2}{k-16}=2$ The equation represents an ellipse if $\mathrm{k}=19$. The equation represents a hyperbola if $\mathrm{k}=12$ The equation…