class 11

Math

Co-ordinate Geometry

Conic Sections

Tangent and normal are drawn at P(16,16) on the parabola $y_{2}=16x$ which intersect the axis of the parabola at A and B respectively. If C is the centre of the circle through the points P,A and B and $∠CPB=θ$ then the value of $tanθ$ is

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Find the equation of the hyperbola satisfying the give conditions: Foci $(0,±13)$ the conjugate axis is of length $24$

Find the equation of the circle with centre $(−a,−b)$ and radius $a_{2}−b_{2} $

If the straight line $xcosα+ysinα=p$ touches the curve $a_{2}x_{2} +b_{2}y_{2} =1$ , then prove that $a_{2}cos_{2}α+b_{2}sin_{2}α=p_{2}˙$

The locus of the midde points ofchords of hyperbola $3x_{2}−2y_{2}+4x−6y=0$ parallel to $y=2x$ is

A line passing through the origin $O(0,0)$ intersects two concentric circles of radii $aandb$ at $PandQ,$ If the lines parallel to the X-and Y-axes through $QandP,$ respectively, meet at point $R,$ then find the locus of $R˙$

Find the equation for the ellipse that satisfies the given conditions: Major axis on the $x$-axis, centre is origin and passes through the points $(4,3)$ and $(6,2).$

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

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.