class 11

Math

Co-ordinate Geometry

Conic Sections

Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length $27 $ on y-axis is (are)

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If $SandS_{′}$ are two foci of ellipse $16x_{2}+25y_{2}=400andPSQ$ is a focal chord such that $SP=16,$ then find $S_{prime}Q˙$

Find the area of the greatest isosceles triangle that can be inscribed in the ellipse $(a_{2}x_{2} )+(b_{2}y_{2} )=1$ having its vertex coincident with one extremity of the major axis.

Find the equation of an ellipse whose axes are the x-and y-axis and whose one focus is at (4,0) and eccentricity is 4/5.

The coordinates of the vertices $BandC$ of a triangle $ABC$ are (2, 0) and (8, 0), respectively. Vertex $A$ is moving in such a way that $42tanB 2tanC =1.$ Then find the locus of $A$

Find the equation of a circle with centre $(2,2)$ and passes through the point $(4,5)$.

Find the equation of the hyperbola satisfying the give conditions: Foci $(±4,0)$ the latus rectum is of length $12$

If $ax +by =2 $ touches the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ , then find the eccentric angle $θ$ of point of contact.

If the chords of contact of tangents from two poinst $(x_{1},y_{1})$ and $(x_{2},y_{2})$ to the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ are at right angles, then find the value of $y_{1}y_{2}x_{1}x_{2} ˙$