Hyperbola PYQs - Last 10 Years

Consider the ellipse $E$ given by $\frac{x^2}{18}+\frac{y^2}{12}=1$. Let $H$ be the hyperbola whose eccentricity is the reciprocal of the eccentricity of $E$ and whose foci are the same as that of $E$. Let $P$ and $Q$ be the points of inter...

Match each entry in List-I to the correct entry in List-II and choose the correct option.






List-I

List-II











(P) The circle with centre $(1,2)$ and touching the straight line

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Consider the hyperbola

\(\frac{x^{2}}{100}-\frac{y^{2}}{64}=1\)

with foci at $S$ and $S_{1}$, where $S$ lies on the positive $x$-axis. Let $P$ be a point on the hyperbola, in the first quadrant. Let $\angle S P S_{1}=\alpha$, with $\alp...

Let a and b be positive real numbers such that a > 1 and b < a. Let P be a point in the first quadrant that lies on the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\). Suppose the tangent to the hyperbola at P passes th...

Let T be the line passing through the points P(\(-\)2, 7) and Q(2, \(-\)5). Let F1 be the set of al pairs of circles (S1, S2) such that T is tangent to S1 at P and tangent to S2 at Q, and also such that S1 and S2 touch each other at a point...

Let \(H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\), where a > b > 0, be a hyperbola in the XY-plane whose conjugate axis LM subtends an angle of 60\(^\circ\) at one of its vertices N. Let the area of the \(\Delta\)LMN be $$4\...

For \(a = \sqrt 2\), if a tangent is drawn to a suitable conic (Column 1) at the point of contact (\(-\)1, 1), then which of the following options is the only CORRECT combination for obtaining its equation?

The tangent to a suitable conic (Column 1) at \(\left( {\sqrt 3 ,\,{1 \over 2}} \right)\) is found to be \(\sqrt 3 x + 2y = 4\), then which of the following options is the only CORRECT combination?

If \(2x - y + 1 = 0\) is a tangent to the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {16}} = 1\) then which of the following CANNOT be sides of a right angled triangle?