class 11

Math

Co-ordinate Geometry

Conic Sections

The circle passing through (1, -2) and touching the axis of x at (3, 0) also passes through the point

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If any tangent to the ellipse $a_{∘}x_{2} +b_{2}y_{2} =1$ intercepts equal lengths $l$ on the axes, then find $l˙$

Prove that the area bounded by the circle $x_{2}+y_{2}=a_{2}$ and the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ is equal to the area of another ellipse having semi-axis $a−b$ and $b,a>b$ .

If the foci of an ellipse are $(0,±1)$ and the minor axis is of unit length, then find the equation of the ellipse. The axes of ellipse are the coordinate axes.

P is the point on the ellipse is$16x_{2} +9y_{2} =1andQ$ is the corresponding point on the auxiliary circle of the ellipse. If the line joining the center C to Q meets the normal at P with respect to the given ellipse at K, then find the value of CK.

Which of the following can be slope of tangent to the hyperbola $4x_{2}−y_{2}=4?$ 1 (b) $−3$ (c) 2 (d) $−23 $

Find the equation of the hyperbola satisfying the give conditions: Foci $(0,±13)$ the conjugate axis is of length $24$

Find the coordinates of the focus, axis of the parabola ,the equation of directrix and the length of the latus rectum for $x_{2}=−9y$

Find the equation of the hyperbola satisfying the given conditions: Foci $(±35 ,0)$ the latus rectum is of length $8$