Class 11

Math

Co-ordinate Geometry

Conic Sections

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

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Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.

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

If a vertex of a triangle is $(1,1)$ , and the middle points of two sides passing through it are $−2,3)$ and $(5,2),$ then find the centroid and the incenter of the triangle.

If TP and TQ are the two tangents to a circle with centre O so that $∠POQ=110_{∘}$, then $∠PTQ$ is equal to

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

A straight line is drawn through $P(3,4)$ to meet the axis of $x$ and $y$ at $AandB$ , respectively. If the rectangle $OACB$ is completed, then find the locus of $C˙$

Two points P(a,0) and Q(-a,0) are given. $R$ is a variable point on one side of the line $PQ$ such that $∠RPQ−∠RQP$ is a positive constant $2α˙$ Find the locus of the point $R˙$

If the middle points of the sides of a triangle are $(−2,3),(4,−3),and(4,5)$ , then find the centroid of the triangle.