Maths NCERT Exemplar Solutions Class 12th Chapter Eleven

The equation of a common tangent to the parabolas y = x² and y = -(x – 2)² is

The acute angle between the pair of tangents drawn to the ellipse 2x² + 3y² = 5 from the point (1, 3) is

Two tangent lines ${\mathcal{l}}_{1}and{\mathcal{l}}_2$ are drawn from the point (2, 0) to the parabola 2y² = x. If the lines ${\mathcal{l}}_{1}and{\mathcal{l}}_2$ are also tangent to the circle (x – 5)² + y²= r, then 17r is equal to……….

Let the tangents at the points P and Q on the ellipse $\frac{x^2}{2}+\frac{y^2}{4}=1$ meet at the point $R\left(\sqrt[]{2},2\sqrt[]{2}-2\right).$ If S is the focus of the ellipse on its negative major axis, then SP² + SQ² is equal to………

A horizontal park is in the shape of a triangle OAB with AB = 16. A vertical lamp post OP is erected at the point O such that $\angle PAO=\angle PBO=15°and\angle PCO=45°,$ where C is the midpoint of AB. Then (OP)² is equal to

A plane P is parallel to two lines whose direction ratios are 2, 1 3 and 1, 2, 2 and it contains the point (2, 2, 2). Let P intersect the co-ordinate axes at the points A, B, C making the intercepts $\alpha ,\beta ,\gamma .$ If V is the volume of the tetrahedron OABC, where O is the origin, and p = $\mathrm{\alpha +}$
$\beta$+ $\gamma$ , then the ordered pair (V, p) is equal to:

Let the lines $\frac{x-1}{\lambda }=\frac{y-2}{1}=\frac{z-3}{2}and\frac{x+26}{-2}=\frac{y+18}{3}=\frac{z+28}{\lambda }$ be coplanar and P be the plane containing these two lines. Then which of the following points does NOT lie on P?

Let the hyperbola H : $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ pass through the point $\left(2\sqrt[]{2},-2\sqrt[]{2}\right).$ A parabola is drawn whose focus is same as the focus of H with positive abscissa and the directrix of the parabola passes through the other focus of H. If the length of the latus rectum of the parabola is e times the length of the latus rectum of H, where e is the eccentricity of H, then which of the following points lies on the parabola?

Let the tangents at two points A and B on the circle x² + y² – 4x + 3 = 0 meet at origin O(0, 0). Then the area of the triangle OAB is:

If the equation of a plane $P$ , passing through the intersection of the planes, $x+4y-z+7$ $=0$ and $3x+y+5z=8$ is $ax+by+6z=15$ for some $a,b\in R$ , then the distance of the point $(\mathrm{3,2},-1)$ from the plane $P$ is(