If a number of ellipse be described having the same major axis $2a$ but a variable minor axis then the tangents at the ends of their latera recta pass through fixed points which can be
$(0, a)$
$(0, - a)$
$(0, 0)$
both $(A)$ and $(B)$
The eccentricity of the ellipse $4{x^2} + 9{y^2} + 8x + 36y + 4 = 0$ is
If the point of intersections of the ellipse $\frac{ x ^{2}}{16}+\frac{ y ^{2}}{ b ^{2}}=1$ and the circle $x ^{2}+ y ^{2}=4 b , b > 4$ lie on the curve $y^{2}=3 x^{2},$ then $b$ is equal to:
Eccentricity of the conic $16{x^2} + 7{y^2} = 112$ is
An ellipse having foci at $(3, 1)$ and $(1, 1) $ passes through the point $(1, 3),$ then its eccentricity is
An arch is in the form of a semi-cllipse. It is $8 \,m$ wide and $2 \,m$ high at the centre. Find the height of the arch at a point $1.5\, m$ from one end.