Question

$\begin{array}{cccc}& ListI& & ListII\\ P.& Distancebetweenfociofthecurve& 1.& \sqrt{7}\\ & x=1+4cos\theta ,y=2+3sin\theta is& & \\ Q.& Areaofthegreatestrectangle& 2.& 8\sqrt{7}\\ & thatcanbeinscribedin& & \\ & \frac{x^2}{16}+\frac{y^2}{7}=1is& & \\ R.& Iftheline3x+4y=\sqrt{7}touches& 3.& 3\sqrt{7}\\ & theellipse3x^2+4y^2=1atP(\alpha ,\beta )& & \\ & then\frac{2}{\alpha }+\frac{1}{\beta }=& & \\ S.& Ifthefociof\frac{x^2}{16}+\frac{y^2}{b^2}=1& 4.& 2\sqrt{7}\\ & and\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}coincide,& & \\ & thenthevalueof{}^{\prime }{b}^{\prime }is& & \end{array}$

• A. P-2; Q-1; R-3; S-4
• B. P-4; Q-2; R-3; S-1
• C. P-1; Q-3; R-2; S-4
• D. P-4; Q-3; R-2; S-1

Answer 1

The correct option is B P-4; Q-2; R-3; S-1

(P) Given Equations: $\frac{(x-1{)}^2}{16}+\frac{(y-2{)}^2}{9}=1a^2=16,b^2=9\Rightarrow e=\frac{\sqrt{7}}{4}S{S}^{\prime }=2ae=2\sqrt{7}$
(Q) Max area $=2ab=2\left(4\right)\left(\sqrt{7}\right)=8\sqrt{7}$
(R) $P(\alpha ,\beta )=(-\frac{a^{2}l}{n},-\frac{b^{2}l}{n})=(\frac{1}{\sqrt{7}},\frac{1}{\sqrt{7}})$
(S) For hyperbola, $\frac{e=\sqrt{a^2+b^2}}{a^2}=\frac{5}{4}$
$Foci=(\pm ae,0)=(\pm 3,0)$
For ellipse, $ae=3$
$b^2=a^2(1-e^2)=a^2-a^2{e}^2=16-9=7$