Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the maximum area of the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ which touches the line $y=3x+2.$

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

The vertices of a triangle are $A(−1,−7),B(5,1)andC(1,4)˙$ If the internal angle bisector of $∠B$ meets the side $AC$ in $D,$ then find the length $AD˙$

Find the centre and the radius of the circle $x_{2}+y_{2}+8x+10y−8=0$.

If $P$ divides $OA$ internally in the ratio $λ_{1}:λ_{2}$ and $Q$ divides $OA$ externally in the ratio $λ_{1};λ_{2},$ then prove that $OA$ is the harmonic mean of $OP$ and $OQ˙$

If $ABC$ having vertices $A(acosθ_{1},asinθ_{1}),B(acosθ_{2}asinθ_{2}),andC(acosθ_{3},asinθ_{3})$ is equilateral, then prove that $cosθ_{1}+cosθ_{2}+cosθ_{3}=sinθ_{1}+sinθ_{2}+sinθ_{3}=0.$

Find the equation for the ellipse that satisfies the given conditions:Vertices $(0,±13),$foci $(0,±5)$

Prove that the area of the triangle whose vertices are $(t,t−2),(t+2,t+2),$ and $(t+3,t)$ is independent of $t˙$

Find the equations of the hyperbola satisfying the given conditions :Vertices $(0,±3),foci(0,±5)$