The tangent at a point `P(acosvarphi,bsinvarphi)` of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` meets its auxiliary circle at two points, the chord joining which subtends a right angle at the center. Find the eccentricity of the ellipse.

The tangent at the point alpha on the ellipse x^2/a^2+y^2/b^2=1 meets the auxiliary circle in two points which subtends a right angle at the centre, then the eccentricity 'e' of the ellipse is given by the equation (A) e^2(1+cos^2alpha)=1 (B) e^2(cosec^2alpha-1)=1 (C) e^2(1+sin^2alpha)=1 (D) e^2(1+tan^2alpha)=1

From any point on any directrix of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,a > b , a pari of tangents is drawn to the auxiliary circle. Show that the chord of contact will pass through the correspoinding focus of the ellipse.

Find the locus of the mid point of the circle x^2+y^2=a^2 which subtend a right angle at the point (p,q)

The locus of the point, the chord of contact of which wrt the circle x^(2)+y^(2)=a^(2) subtends a right angle at the centre of the circle is

The line x = at^(2) meets the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 in the real points iff

If the normal at any point P on ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 meets the auxiliary circle at Q and R such that /_QOR = 90^(@) where O is centre of ellipse, then

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.

Find the locus of the midpoint of the chords of the circle x^2+y^2=a^2 which subtend a right angle at the point (c ,0)dot

Find the locus of the midpoint of the chords of the circle x^2+y^2=a^2 which subtend a right angle at the point (0,0)dot

Two parallel tangents of a circle meet a third tangent at points P and Q. Prove that PQ subtends a right angle at the centre.