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 for the ellipse that satisfies the given conditions: $b=3,ae=4$ centre at the origin; foci on the $x$- axis.

Find the slope of a common tangent to the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ and a concentric circle of radius $r˙$

The locus a point $P(α,β)$ moving under the condition that the line $y=αx+β$ is a tangent to the hyperbola $a_{2}x_{2} −b_{2}y_{2} =1$ is (A) a parabola (B) an ellipse (C) a hyperbola (D) a circle

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and $100m$ long is supported by vertical wires attached to the cable the longest wire being $30m$ and the shortest being $6m$. Find the length of a supporting wire attached to the roadway $18m$ from the middle.

Find the equation of the chord of the hyperbola $25x_{2}−16y_{2}=400$ which is bisected at the point (5, 3).

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 $(1,6).$

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 $ANPN_{2} A˙_{prime}N˙$

Find the equation of the parabola that satisfies the following conditions: Focus $(6,0)$; directrix $x=−6$