Class 11

Math

Co-ordinate Geometry

Conic Sections

The length of the major axis of the ellipse $(5x−10)_{2}+(5y+15)_{2}=4(3x−4y+7)_{2} $ is

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

Find the centre and radius of the circles$x_{2}+y_{2}−8x+10y−12=0$

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.$x_{2}=−16y$

Shift the origin to a suitable point so that the equation $y_{2}+4y+8x−2=0$ will not contain a term in $y$ and the constant term.

In any triangle ABC, if the angle bisector of $∠A$and perpendicular bisector of BCintersect, prove that they intersect on the circumcircle of the triangle ABC

Find the equation of the parabola with vertex at origin, symmetric with respect to y-axis and passing through $(2,−3)$

Find the locus of the point $(t_{2}−t+1,t_{2}+t+1),t∈R˙$

Find the area of the quadrilateral $ABCD$ having vertices $A(1,1),B(7,−3),C(12,2),$ and $D(7,21)˙$