class 11

Math

Co-ordinate Geometry

Conic Sections

Let A and B be two distinct points on the parabola $y_{2}=4x$. If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be

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If $PSQ$ is a focal chord of the ellipse $16x_{2}+25y_{2}=400$ such that $SP=8,$ then find the length of $SQ.$ is (a) $21 $ (b) $94 $ (c) $98 $ (d) $916 $

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the rectum for $y_{2}=12x$

Find the equation of the parabola that satisfies the following conditions: Focus $(0,−3)$; directrix $y=3$

A point $P$ moves such that the chord of contact of the pair of tangents from $P$ on the parabola $y_{2}=4ax$ touches the rectangular hyperbola $x_{2}−y_{2}=c_{2}˙$ Show that the locus of $P$ is the ellipse $c_{2}x_{2} +(2a)_{2}y_{2} =1.$

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 form the vertex of the parabola?

Find the equation of the parabola that satisfies the following conditions: Vertex $(0,0)$ passing through $(5,2)$ and symmetric with respect to $y$- axis

If the normal at one end of the latus rectum of the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ passes through one end of the minor axis, then prove that eccentricity is constant.

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