Class 11

Math

Co-ordinate Geometry

Conic Sections

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

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Given that $A(1,1)$ and $B(2,−3)$ are two points and $D$ is a point on $AB$ produced such that $AD=3AB˙$ Find the coordinates of $D˙$

If $A(cosα,sinα),B(sinα,−cosα),C(1,2)$ are the vertices of $ABC,$ then as $α$ varies, find the locus of its centroid.

Shift the origin to a suitable point so that the equation $y_{2}+4y+8x−2=0$ will not contain a term in $y$ and the constant term.

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.

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

Orthocenter and circumcenter of a $DeltaABC$ are $(a,b)and(c,d)$ , respectively. If the coordinates of the vertex $A$ are $(x_{1},y_{1}),$ then find the coordinates of the middle point of $BC˙$

Find the equation for the ellipse that satisfies the given conditions:Ends of major axis $(0,±5 )$, ends of minor axis $(±1,0)$