Class 11

Math

Co-ordinate Geometry

Conic Sections

Tangent drawn from the point $P(4,0)$ to the circle $x_{2}+y_{2}=8$ touches it at the point $A$ in the first quadrant. Find the coordinates of another point $B$ on the circle such that $AB=4$ .

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If $P$ divides $OA$ internally in the ratio $λ_{1}:λ_{2}$ and $Q$ divides $OA$ externally in the ratio $λ_{1};λ_{2},$ then prove that $OA$ is the harmonic mean of $OP$ and $OQ˙$

In any triangle ABC, if the angle bisector of $∠A$and perpendicular bisector of BCintersect, prove that they intersect on the circumcircle of the triangle ABC

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 $BC˙$

The equation of curve referred to the new axes, axes retaining their directions, and origin $(4,5)$ is $X_{2}+Y_{2}=36$ . Find the equation referred to the original axes.

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.$x_{2}=6y$

Find the locus of the point $(t_{2}−t+1,t_{2}+t+1),t∈R˙$

Find the equation for the ellipse that satisfies the given conditions:Vertices $(±5,0)$, foci $(±4,0)$

If $A(2,−1)andB(6,5)$ are two points, then find the ratio in which the food of the perpendicular from $(4,1)$ to $AB$ divides it.