Class 10

Math

All topics

Conic Sections

In the given figure, triangle ABC is circumscribing a circle. Find the length of BC, if AF=3 cm, FB=4 cm and AC= 9 cm

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If $F_{1}$ and $F_{2}$ are the feet of the perpendiculars from the foci $S_{1}andS_{2}$ of the ellipse $25x_{2} +16y_{2} =1$ on the tangent at any point $P$ on the ellipse, then prove that $S_{1}F_{1}+S_{2}F_{2}≥8.$

Find the area of the greatest rectangle that can be inscribed in an ellipse $a_{2}x_{2} +b_{2}y_{2} =1$

An ellipse has $OB$ as the semi-minor axis, $FandF_{′}$ as its foci, and $∠FBF_{′}$ a right angle. Then, find the eccentricity of the ellipse.

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

If the tangent to the ellipse $x_{2}+2y_{2}=1$ at point $P(2 1 ,21 )$ meets the auxiliary circle at point $RandQ$ , then find the points of intersection of tangents to the circle at $QandR˙$

The tangent at a point $P$ on an ellipse intersects the major axis at $T,andN$ is the foot of the perpendicular from $P$ to the same axis. Show that the circle drawn on $NT$ as diameter intersects the auxiliary circle orthogonally.

Find the equation of the parabola that satisfies the following conditions: Vertex $(0,0)$ passing through $(2,3)$ and axis is along $x$-axis

If the focal distance of an end of the minor axis of an ellipse (referred to its axes as the axes of $xandy$ , respectively) is $k$ and the distance between its foci is $2h,$ them find its equation.