Class 11

Math

Co-ordinate Geometry

Conic Sections

The slopes of the common tanents of the ellipse $4x_{2} +1y_{2} =1$ and the circle $x_{2}+y_{2}=3$ are $±1$ (b) $±2 $ (c) $±3 $ (d) none of these

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A quadrilateral ABCD is drawn to circumscribe a circle. Prove that $AB+CD=AD+BC$

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length TP.

Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.$5y_{2}−9x_{2}=36$

Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.$9y_{2}−4x_{2}=36$

The coordinates of the point $AandB$ are (a,0) and $(−a,0),$ respectively. If a point $P$ moves so that $PA_{2}−PB_{2}=2k_{2},$ when $k$ is constant, then find the equation to the locus of the point $P˙$

A rod of length $l$ slides with its ends on two perpendicular lines. Find the locus of its midpoint.

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.