Embibe Experts Solutions for Chapter: Conic Section, Exercise 2: Exercise

If the ellipse $\frac{x^2}{a^2-7}+\frac{y^2}{13-5a}=1$ is inscribed in a square of side length $\sqrt{2}a$, then $a$ is equal to

The normal at a variable point $P$ on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ of eccentricity $e$ meets the axes of the ellipse at $Q$ and $R,$ then the locus of the midpoint of $QR$ is a conic with an eccentricity $e^{\text{'}}$ such that

The asymptote of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ form with any tangent to the hyperbola a triangle whose area is $a^2\tan \lambda$ in magnitude then its eccentricity is

If two points $P$ and $Q$ on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1,$ whose centre $C$ be such that $CP$ is perpendicular to $CQ, a<b,$  then the value of $\frac{1}{C{P}^2}+\frac{1}{C{Q}^2}$ is

The equation of the chord joining two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ on the rectangular hyperbola $xy=c^2$ is

Let $\text{'}C\text{'}$ be a curve which is locus of the point of the intersection of lines $x=2+m$ and $my=4-m.$ A circle $s\equiv (x-2{)}^2+(y+1{)}^2=25$ intersects the curve $C$ at four points $P, Q, R$ and $S.$ If $O$ is centre of the curve $\text{'}C\text{'},$ then $O{P}^2+O{Q}^2+O{R}^2+O{S}^2$ is

The angle between lines joining the origin to the points of intersection of the line $\sqrt{3}x+y=2$ and the curve $y^2-x^2=4$ is

The exhaustive set of values of $a^2$ such that there exists a tangent to the ellipse $x^2+a^2{y}^2=a^2$ such that the portion of the tangent intercepted by the hyperbola $a^2{x}^2-y^2=1$ subtends a right angle at the centre of the curves is