New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Hyperbola question

2024 · 8 Apr · Shift 1 · Q37

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

PYQ Library
JEE Main
Mathematics
Hyperbola
2024 · 8 Apr · Shift 1 · Q37

Hyperbola question

2024 · 8 Apr · Shift 1 · Q37

JEE MainMathematicsHyperbolaMCQ+4 / −1

Let

H: \frac{-x^2}{a^2}+\frac{y^2}{b^2}=1

be the hyperbola, whose eccentricity is

\sqrt{3}

and the length of the latus rectum is

4 \sqrt{3}

. Suppose the point

(\alpha, 6), \alpha\gt 0

lies on

H

. If

\beta

is the product of the focal distances of the point

(\alpha, 6)

, then

\alpha^2+\beta

is equal to

A
170
B
171
C
169
D
172

More from Hyperbola

Let $S$ be the focus of the hyperbola $\frac{x ^{2}}{3} - \frac{y ^{2}}{5} = 1$ , on the positive $x$ -axis. Let $C$ be the circle with its centre at $A (6, 5)$ and passing through the point $S$ . If $O$ …2024 · Numerical
Let the foci of a hyperbola $H$ coincide with the foci of the ellipse $E : \frac{( x - 1 ) ^{2}}{100} + \frac{( y - 1 ) ^{2}}{75} = 1$ and the eccentricity of the hyperbola $H$ be the reciprocal of the eccentricity of the ellipse $E$ . If the length of the…2024 · MCQ
Let $e_{1}$ be the eccentricity of the hyperbola $\frac{x ^{2}}{16} - \frac{y ^{2}}{9} = 1$ and $e_{2}$ be the eccentricity of the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1, a > b$ , which passes through the foci of the hyperbola.…2024 · MCQ
Let the latus rectum of the hyperbola $\frac{x ^{2}}{9} - \frac{y ^{2}}{b ^{2}} = 1$ subtend an angle of $\frac{π}{3}$ at the centre of the hyperbola. If $b^{2}$ is equal to $\frac{l}{m} (1 + n)$ , where $l$ and $m$ …2024 · Numerical
Let $P$ be a point on the hyperbola $H : \frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1$ , in the first quadrant such that the area of triangle formed by $P$ and the two foci of $H$ is $213$ . Then, the square of the distance of $P$ from the origin is2024 · MCQ
If the foci of a hyperbola are same as that of the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{25} = 1$ and the eccentricity of the hyperbola is $\frac{15}{8}$ times the eccentricity of the ellipse, then the smaller focal distance of the point $(2, \frac{14}{3} \frac{2}{5})$ …2024 · MCQ
Let the foci and length of the latus rectum of an ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1, a > bb e (\pm 5, 0)$ and $50$ , respectively. Then, the square of the eccentricity of the hyperbola $\frac{x ^{2}}{b ^{2}} - \frac{y ^{2}}{a ^{2} b ^{2}} = 1$ …2024 · Numerical
Let the eccentricity of an ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ is reciprocal to that of the hyperbola $2 x^{2} - 2 y^{2} = 1$ . If the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum…2023 · Numerical