Class 11

Math

Co-ordinate Geometry

Conic Sections

Prove that the chords of contact of pairs of perpendicular tangents to the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ touch another fixed ellipse.

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If two equal chords of a circle intersect within the circle, prove that the segments ofone chord are equal to corresponding segments of the other chord.

Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line $4x+y=16$.

A variable line through point $P(2,1)$ meets the axes at $AandB$ . Find the locus of the circumcenter of triangle $OAB$ (where $O$ is the origin).

The three points $(−2,2)(9,−2),and(−4,−3)$ are the vertices of (a) an isosceles triangle (b) an equilateral triangle (c) a right-angled triangle (d) none of these

Determine $x$ so that the line passing through $(3,4)and(x,5)$ makes an angle of $135_{0}$ with the positive direction of the x-axis.

The focus of a parabolic mirror as shown in is at a distance of 5 cm from its vertex. If the mirror is 45 cm deep, find the distance AB

Find the equation for the ellipse that satisfies the given conditions:Vertices $(0,±13),$foci $(0,±5)$

Find the equation of the parabola with vertex at (0, 0) and focus at (0, 2).