Class 12

Math

Co-ordinate Geometry

Conic Sections

Length of the focal chord of the parabola $(y+3)_{2}=−8(x−1)$ which lies at a distance 2 units from the vertex of the parabola is

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Find the eccentric angle of a point on the ellipse $6x_{2} +2y_{2} =1$ whose distance from the center of the ellipse is $5 $

Find the coordinates of the foci, the vertices the eccentricity and the length of latus rectum of the hyperbola $9y_{2}−4x_{2}=36$

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

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse $100x_{2} +400y_{2} =1.$

How many real tangents can be drawn from the point (4, 3) to the hyperbola $16x_{2} −9y_{2} =1?$ Find the equation of these tangents and the angle between them.

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 $b,a>b$ .

An arc of a bridge is semi-elliptical with the major axis horizontal. If the length of the base is 9m and the highest part of the bridge is 3m from the horizontal, then prove that the best approximation of the height of the acr 2 m from the center of the base is $38 m˙$

Find the condition on $aandb$ for which two distinct chords of the hyperbola $2a_{2}x_{2} −2b_{2}y_{2} =1$ passing through $(a,b)$ are bisected by the line $x+y=b$ .