# Hyperbola · Mathematics · WB JEE

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WB JEE 2008
If t is a parameter, then $$x = a\left( {t + {1 \over t}} \right)$$, $$y = b\left( {t - {1 \over t}} \right)$$ represents
WB JEE 2010
If the line ax + by + c = 0 is a tangent to the curve xy = 4, then
WB JEE 2010
For different values of $$\alpha$$, the locus of the point of intersection of the two straight lines $$\sqrt 3 x - y - 4\sqrt 3 \alpha = 0$$ and $$\s... WB JEE 2011 The eccentricity of the hyperbola$$4{x^2} - 9{y^2} = 36$$is WB JEE 2024 In a plane$$\vec{a}$$and$$\vec{b}$$are the position vectors of two points A and B respectively. A point P with position vector$$\overrightarrow...
WB JEE 2024
The locus of the midpoint of the system of parallel chords parallel to the line $$y=2 x$$ to the hyperbola $$9 x^2-4 y^2=36$$ is
WB JEE 2023
If a hyperbola passes through the point P($$\sqrt2$$, $$\sqrt3$$) and has foci at ($$\pm$$ 2, 0), then the tangent to this hyperbola at P is
WB JEE 2023
The average length of all vertical chords of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1,a \le x \le 2a$$, is :
WB JEE 2023
Let $$A(2\sec \theta ,3\tan \theta )$$ and $$B(2\sec \phi ,3\tan \phi )$$ where $$\theta + \phi = {\pi \over 2}$$ be two points on the hyperbola $$... WB JEE 2022 Let$$P(3\sec \theta ,2\tan \theta )$$and$$Q(3\sec \phi ,2\tan \phi )$$be two points on$${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1$$such that$$\...
WB JEE 2022
PQ is a double ordinate of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ such that $$\Delta OPQ$$ is an equilateral triangle...
WB JEE 2021
The normal to a curve at P(x, y) meets the X-axis at G. If the distance of G from the origin is twice the abscissa of P then the curve is
WB JEE 2021
The locus of the centre of a variable circle which always touches two given circles externally is
WB JEE 2020
A double ordinate PQ of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ is such that $$\Delta OPQ$$ is equilateral, O being th...
WB JEE 2019
Let P(4, 3) be a point on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. If the normal at P intersects the X-axis at (16, 0)...
WB JEE 2019
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