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

Consider the ellipses given by

Let P be the point in the first quadrant where the given ellipses intersect. If $\theta$ is the acute angle between the tangents to the given ellipses at the point P , then the value of …

Let $P\left(x_1,y_1\right)$ and $Q\left(x_2,y_2\right)$ be two distinct points on the ellipse

such that $y_1>0$, and $y_2>0$. Let C denote the circle $x^2+y^2=9$, and $M$ be the point ( 3,0 ).
Suppose the line …

Consider the ellipse $\frac{{\mathrm{x}}^2}{9}+\frac{{\mathrm{y}}^2}{4}=1$. Let $\mathrm{S}(\mathrm{p},\mathrm{q})$ be a point in the first quadrant such that $\frac{{\mathrm{p}}^2}{9}+\frac{{\mathrm{q}}^2}{4}>1$. Two tangents are drawn from S to the ellipse, of which one …

Consider the ellipse

Let $H(\alpha ,0),0<\alpha <2$, be a point. A straight line drawn through $H$ parallel to the $y$-axis crosses the ellipse and its auxiliary circle at points $E$ and $F$ respectively, in the first quadrant. The tangent t …

Let E be the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$. For any three distinct points P, Q and Q' on E, let M (P, Q) be the mid-point of the line segment joining P and Q , and $\mathrm{M}\left(\mathrm{P},{\mathrm{Q}}^{\prime }\right)$ be the mid-point of the line segment joining …

Let a, b and $\lambda$ be positive real numbers. Suppose P is an end point of the latus rectum of the parabola $y^2=4\lambda x$, and suppose the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ passes through the point P. If the tangents to the parabola and the ellipse at th …