Class 10

Math

All topics

Conic Sections

In Figure 3, a circle touches all the four sides of a quadrilateral ABCDwhose sides are AB = 6 cm, BC = 9 cm and CD = 8 cm. Find the length of side AD.

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

Find the point on the ellipse $16x_{2}+11y_{2}=256$ where the common tangent to it and the circle $x_{2}+y_{2}−2x=15$ touch.

For an ellipse $9x_{2} +4y_{2} =1$ with vertices A and A', drawn at the point P in the first quadrant meets the y axis in Q and the chord A'P meets the y axis in M. If 'O' is the origin then $OQ_{2}−MQ_{2}$

The ratio of the area of triangle inscribed in ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ to that of triangle formed by the corresponding points on the auxiliary circle is 0.5. Then, find the eccentricity of the ellipse. (A) $21 $ (B) $23 $ (C) $2 1 $ (D) $3 1 $

Find the locus of the middle points of all chords of $4x_{2} +9y_{2} =1$ which are at a distance of 2 units from the vertex of parabola $y_{2}=−8ax˙$

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.

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 $36x_{2} +16y_{2} =1.$

If the normals to the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ at the points $(X_{1},y_{1}),(x_{2},y_{2})and(x_{3},y_{3})$ are concurrent, prove that $∣∣ x_{1}x_{2}x_{3} y_{1}y_{2}y_{3} x_{1}y_{1}x_{2}y_{2}x_{3}y_{3} ∣∣ =0$.