List of top Mathematics Questions on Hyperbola asked in AP EAPCET

If \(C\) is the centre of the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] and the tangent drawn at any point \(P\) on the hyperbola meets the lines \[ bx-ay=0 \] and \[ bx+ay=0 \] at \(Q\) and \(R\) respectively, then \[ CQ\cdot CR= \]

From a point \[ P(x_1,-1), \qquad (x_1<0), \] two tangents are drawn to the hyperbola \[ \frac{x^2}{2}-\frac{y^2}{3}=1. \] If the sum of the slopes of the tangents is \(2\), then \(x_1=\)

Consider the hyperbola \[ S \equiv \frac{x^2}{25}-\frac{y^2}{16}-1=0. \] Let \(B,B'\) be the ends of the transverse axis of the conjugate hyperbola of \(S=0\). If \(C\) is the circle with \(B,B'\) as ends of a diameter, then the slope of a common tangent to \(C\) and the given hyperbola is:

The eccentricity of the hyperbola \[ 16x^2-9y^2=144 \] is

Let \[ x^2+y^2=16 \] be the equation of the auxiliary circle of a hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] and let \((4\sqrt{2},3)\) be a point on the hyperbola. Then the eccentricity of the hyperbola is

The distance between the tangent lines to the hyperbola \[ x^2-2y^2=18 \] which are perpendicular to the line \(y=x\) is

Let \(L(x_1,4)\) be the end of the latus rectum of the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] lying in the first quadrant and let \(S(8,y_1)\) be the focus of the given hyperbola. Then the length of its transverse axis is:

If the line \(3x-my+5=0\) is a tangent to the hyperbola \(3x^2-4y^2=300\), then the square of the \(Y\)-intercept made by this tangent line is

If \[ \sqrt{5}y-\sqrt{8}=0 \] is the equation of the directrix of a hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}+1=0 \] and \[ \frac{\sqrt{5}}{2} \] is its eccentricity, then \[ a= \] is:

The locus of the point of intersection of the tangents at the end-points of normal chords of the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] is

If \(e_1\) and \(e_2\) are the eccentricities of the hyperbola \[ 16x^2-9y^2=1 \] and its conjugate respectively, then \(3e_1=\)

The locus of point of intersection of tangents at the ends of normal chord of the hyperbola \[ x^2-y^2=a^2 \] is

If the vertices and foci of a hyperbola are respectively \((\pm 3,0)\) and \((\pm 4,0)\), then the parametric equations of that hyperbola are

If the normal to the rectangular hyperbola \[ x^2-y^2=1 \] at the point \(P\left(\frac{\pi}{4}\right)\) meets the curve again at \(Q(\theta)\), then \[ \sec^2\theta+\tan\theta= \]