If the normal at any point P on the ellipse a2x2+b2y2=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 x2+y2=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 (a2+1,a2+1)
then find the orthocentre.
having vertices A(acosθ1,asinθ1),B(acosθ2asinθ2),andC(acosθ3,asinθ3)
is equilateral, then prove that cosθ1+cosθ2+cosθ3=sinθ1+sinθ2+sinθ3=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.