New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Hyperbola question

2007 · Shift 1 · Q28

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Mathematics
Hyperbola
2007 · Shift 1 · Q28

Hyperbola question

2007 · Shift 1 · Q28

JEE AdvancedMathematicsHyperbolaMCQ+3 / −1

A hyperbola, having the transverse axis of the length

2\sin \theta

, is confocal with the ellipse

3{x^2} + 4{y^2} = 12

. Then its equation is

A
${x^2}\cos e{c^2}\theta - {y^2}{\sec ^2}\theta = 1$
B
${x^2}{\sec ^2}\theta - {y^2}\cos e{c^2}\theta = 1$
C
${x^2}{\sin ^2}\theta - {y^2}{\cos ^2}\theta = 1$
D
${x^2}{\cos ^2}\theta - {y^2}{\sin ^2}\theta = 1$

More from Hyperbola

Consider the hyperbola $\frac{x ^{2}}{100} - \frac{y ^{2}}{64} = 1$ with foci at $S$ and $S_{1}$ , where $S$ lies on the positive $x$ -axis. Let $P$ be a point on the hyperbola, in the first quadrant. Let $∠ S P S_{1} = α$ , with $α < \frac{π}{2}$ …2022 · Numerical
Let a and b be positive real numbers such that a > 1 and b < a. Let P be a point in the first quadrant that lies on the hyperbola $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ . Suppose the tangent to the hyperbola at P…2020 · Multiple correct
Let T be the line passing through the points P( $-$ 2, 7) and Q(2, $-$ 5). Let F1 be the set of al pairs of circles (S1, S2) such that T is tangent to S1 at P and tangent to S2 at Q, and also such that S1 and S2 touch each other at a point,…2018 · Multiple correct
Let $H : \frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ , where a > b > 0, be a hyperbola in the XY-plane whose conjugate axis LM subtends an angle of 60 $Δ$ at one of its vertices N. Let the area of the $Δ$ LMN be $43$ … Includes table2018 · MCQ
If $2 x - y + 1 = 0$ is a tangent to the hyperbola $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{16} = 1$ then which of the following CANNOT be sides of a right angled triangle?2017 · Multiple correct
By appropriately matching the information given in the three columns of the following table. Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively. For $a = 2$ , if a tangent is… Includes table2017 · MCQ
By appropriately matching the information given in the three columns of the following table. Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively. The tangent to a suitable conic… Includes table2017 · MCQ
Consider the hyperbola $H : x^{2} - y^{2} = 1$ and a circle $S$ with center $N (x_{2}, 0)$ . Suppose that $H$ and $S$ touch each other at a point $P (x_{1}, y_{1})$ with $x_{1} > 1$ and $y_{1} > 0$ . The…2015 · Multiple correct