Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the standard equation of the ellipse whose foci are $(±2,0)$ and eccentricity 1/2

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Find the equation of the curve whose parametric equation are $x=1+4cosθ,y=2+3sinθ,θ∈R˙$

If the chord joining points $P(α)andQ(β)$ on the ellipse $(a_{2}x_{2} )+(b_{2}y_{2} )=1$ subtends a right angle at the vertex $A(a,0),$ then prove that $tan(2a )tan(2β )=−a_{2}b_{2} ˙$

Find the equation of the circle with centre $(0,2)$ and radius $2$

Find the locus of the middle points of chord of an ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ which are drawn through the positive end of the minor axis.

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 $b,a>b$ .

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

From the point $A(4,3),$ tangent are drawn to the ellipse $16x_{2} +9y_{2} =1$ to touch the ellipse at $B$ and $CE˙F$ is a tangent to the ellipse parallel to line $BC$ and towards point $A˙$ Then find the distance of $A$ from $EF˙$

Find the length of major axis, the eccentricity the latus rectum, the coordinate of the centre, the foci, the vertices and the equation of the directrices of following ellipse: $16x_{2} +9y_{2} =1.$