If the normal at any point $P$ on the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ meets the co-ordinate axes in $G$ and $g$ respectively, then $PG:Pg = $
$a:b$
${a^2}:{b^2}$
${b^2}:{a^2}$
$b:a$
The ellipse ${x^2} + 4{y^2} = 4$ is inscribed in a rectangle aligned with the coordinate axes, which in trun is inscribed in another ellipse that passes through the point $(4,0) $ . Then the equation of the ellipse is :
The number of values of $c$ such that line $y = cx + c$, $c \in R$ touches the curve $\frac{{{x^2}}}{4} + \frac{{{y^2}}}{1} = 1$ is
The locus of the point of intersection of the perpendicular tangents to the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$ is
Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse, $\frac{x^{2}}{4}+\frac{y^{2}}{2}=1$ from any of its foci?
Let $'E'$ be the ellipse $\frac{{{x^2}}}{9}$$+$$\frac{{{y^2}}}{4}$ $= 1$ $\& $ $'C' $ be the circle $x^2 + y^2 = 9.$ Let $P$ $\&$ $Q$ be the points $(1 , 2) $ and $(2, 1)$ respectively. Then :