Hyperbola PYQs - Last 5 Years

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

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 \(\overrightarrow{\mathrm{r}}\) moves on that plane in such a way that $$|\overrightarrow{\vec{r}}-\vec{a}|...

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 \({{{x^2}} \over 4} - {{{y^2}} \over 9} = 1\). If (\(\alpha,\beta\)) is the point of interse...

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 :

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 line y = x + 5 touches

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, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies

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 \(\theta + \phi = {\pi \over 2},0 < \theta ,\phi < {\pi \over 2}\). Then the ordinate of...

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

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

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 the centre of the hyperbola. Then the eccentricity e satisfies the relation