Identify the statements which are True.

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Statement $A$: The ellipse is $\frac{x^2}{9} + \frac{y^2}{5} = 1$. Here $a^2 = 9$ and $b^2 = 5$. The director circle is $x^2 + y^2 = a^2 + b^2 = 9

Vedclass · Accepted Answer

All of the above.

Vedclass · Answer

(D) Statement $A$: The ellipse is $\frac{x^2}{9} + \frac{y^2}{5} = 1$. Here $a^2 = 9$ and $b^2 = 5$. The director circle is $x^2 + y^2 = a^2 + b^2 = 9 + 5 = 14$. This is true.Statement $B$: The coordinates of $P$ and $Q$ are $(a \cos 	heta, b \sin 	heta)$ and $(a \cos(	heta + \alpha), b \sin(	heta + \alpha))$. The area of $	riangle OPQ$ is $\frac{1}{2} |x_P y_Q - x_Q y_P| = \frac{1}{2} |ab \cos 	heta \sin(	heta + \alpha) - ab \cos(	heta + \alpha) \sin 	heta| = \frac{1}{2} ab |\sin(	heta + \alpha - 	heta)| = \frac{1}{2} ab |\sin \alpha|$. This is independent of $	heta$. This is true.Statement $C$: This is a standard property of parabolas. The locus of the foot of the perpendicular from the focus to any tangent is the tangent at the vertex. This is true.Since all statements are true,the correct option is $D$.

Column-$I$	Column-$II$
$A$. Circle	$P$. Locus of point $(h, k)$ such that the line $hx + ky = 1$ touches the circle $x^2 + y^2 = 4$
$B$. Parabola	$Q$. Point $z$ in the complex plane satisfies $\|z + 2\| - \|z - 2\| = \pm 3$
$C$. Hyperbola	$R$. Eccentricity of the conic lies in the interval $[1, \infty)$
	$S$. Point $z$ in the complex plane satisfies $Re(z + 1)^2 = \|z\|^2 + 1$

Similar Questions

The square of the slope of a common tangent drawn to the circle $4x^2 + 4y^2 = 25$ and the ellipse $4x^2 + 9y^2 = 36$ is

Let $P$ be a moving point on the circle $x^2 + y^2 - 6x - 8y + 21 = 0$. Then, the maximum distance of $P$ from the vertex of the parabola $x^2 + 6x + y + 13 = 0$ is equal to:

If the product of eccentricities of the ellipse $\frac{x^2}{16}+\frac{y^2}{b^2}=1$ and the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=-1$ is $1$,then $b^2=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module