Class 11

Math

Co-ordinate Geometry

Conic Sections

If the normal at any point P on the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ meets the axes at G and g, respectively, then find the ratio PG :Pg

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If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices ofthe quadrilateral, prove that it is a rectangle

Does the point $(2,5),(3,5)$ lie inside, outside or on the circle $x_{2}+y_{2}=25$?

If the point $(x,−1),(3,y),(−2,3),and(−3,−2)$ taken in order are the vertices of a parallelogram, then find the values of $xandy˙$

If the circumcenter of an acute-angled triangle lies at the origin and the centroid is the middle point of the line joining the points $(a_{2}+1,a_{2}+1)$ and $(2a,−2a),$ then find the orthocentre.

If $ABC$ having vertices $A(acosθ_{1},asinθ_{1}),B(acosθ_{2}asinθ_{2}),andC(acosθ_{3},asinθ_{3})$ is equilateral, then prove that $cosθ_{1}+cosθ_{2}+cosθ_{3}=sinθ_{1}+sinθ_{2}+sinθ_{3}=0.$

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of $80_{∘}$, then $∠POA$ is equal to

Find the equation of the circle which passes through the points $(2,−2)$, and (3,4) and whose centre lies on the line $x+y=2$.

Find an equation of the circle with centre at (0,0) and radius r.