Hyperbola · Mathematics · WB JEE

If t is a parameter, then $$x = a\left( {t + {1 \over t}} \right)$$, $$y = b\left( {t - {1 \over t}} \right)$$ represents

If the line ax + by + c = 0 is a tangent to the curve xy = 4, then

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...

The eccentricity of the hyperbola $$4{x^2} - 9{y^2} = 36$$ is

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...

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

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

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 :

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 $$...

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 $$\...

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...

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

The locus of the centre of a variable circle which always touches two given circles externally is

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...

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)...

For the hyperbola $${{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1$$, which of the following remains fixed when $$\al...

The equation of the directrices of the hyperbola $$3{x^2} - 3{y^2} - 18x + 12y + 2 = 0$$ is

The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then, the eccentricity e is

A point is in motion along a hyperbola $$y = {{10} \over x}$$ so that its abscissa x increases uniformly at a rate of 1 unit per second. Then, the rat...

Let the eccentricity of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ be reciprocal to that of the ellipse x2 + 9y2 = 9, the...

Let P be the foot of the perpendicular from focus S of hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ on the line bx $$-$$ ay = 0...

The line segment joining the foci of the hyperbola $${x^2} - {y^2} + 1 = 0$$ is one of the diameters of a circle. The equation of the circle is

Let A($$-$$ 1, 0) and B(2, 0) be two points. A point M moves in the plane in such a way that $$\angle MBA$$ = 2$$\angle MAB$$. Then, the point M moves...

The line y = x + 5 touches

Equation of a tangent to the hyperbola 5x2 $$-$$ y2 = 5 and which passes through an external point (2, 8) is

A hyperbola, having the transverse axis of length 2sin$$\theta$$ is confocal wit6h the ellipse 3x2 + 4y2 = 12. Its equation is