class 11

Math

Co-ordinate Geometry

Conic Sections

Â·If the normals of the parabola $y_{2}=4x$ drawn at the end points of its latus rectum are tangents to the circle $(x−3)_{2}(y+2)_{2}=r_{2}$ , then the value of $r_{2}$ is

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Find the equation of tangents to the curve $4x_{2}−9y_{2}=1$ which are parallel to $4y=5x+7.$

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

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

The center of an ellipse is $C$ and $PN$ is any ordinate. Point $A,A_{′}$ are the endpoints of the major axis. Then find the value of $ANPN_{2} A˙_{prime}N˙$

If the straight line $xcosα+ysinα=p$ touches the curve $a_{2}x_{2} +b_{2}y_{2} =1$ , then prove that $a_{2}cos_{2}α+b_{2}sin_{2}α=p_{2}˙$

Find the equation for the ellipse that satisfies the given conditions: Centre at $(0,0)$, major axis on the $y$-axis and passes through the points $(3,2)$ and $(1,6).$

Find the equation of the hyperbola satisfying the given conditions: Foci $(±5,0)$ the transverse axis is of length $8$

Find the center and radius of the circle $x_{2}+y_{2}−4x−8y−45=0$