JEE Advanced · 2012 · 08 Apr 2012 · Paper 1 · Hyperbola

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 intersection of H and the parabola …

Consider the hyperbola

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 $\angle SP{S}_1=\alpha$, with $\alpha <\frac{\pi }{2}$. The straight line passing t …

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 $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. Suppose the tangent to the hyperbola at $P$ passes through the point (1,0), and suppo …

Let $H:\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, where $a>b>0$, be a hyperbola in the $xy$-plane whose conjugate axis $LM$ subtends an angle of $60^0$ at one of its vertices $N$. Let the area of the triangle $LMN$ be $4\sqrt{3}$.
| LIST-I | | LIST-II | || …

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

| (II) $x^2+a^2{y}^2=a^2$ | (ii) $y=mx+a\sqrt{m^2+1}$ | (Q) …