Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the points on the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ such that the tangent at each point makes equal angles with the axes.

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An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices ofthe quadrilateral, prove that it is a rectangle

If a vertex, the circumcenter, and the centroid of a triangle are (0, 0), (3,4), and (6, 8), respectively, then the triangle must be (a) a right-angled triangle (b) an equilateral triangle (c) an isosceles triangle (d) a right-angled isosceles triangle

Convert $r=cosecθe_{rcosθ}$ into its equivalent Cartesian equation.

At what point should the origin be shifted if the coordinates of a point $(4,5)$ become $(−3,9)?$

The line joining the points $(x,2x)and(3,5)$ makes an obtuse angle with the positive direction of the x-axis. Then find the values of $x˙$

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

If $P$ divides $OA$ internally in the ratio $λ_{1}:λ_{2}$ and $Q$ divides $OA$ externally in the ratio $λ_{1};λ_{2},$ then prove that $OA$ is the harmonic mean of $OP$ and $OQ˙$