Let `x^2/a^2+y^2/b^2=1 and x^2/A^2-y^2/B^2=1` be confocal `(a > A and a> b)` having the foci at `s_1 and S_2,` respectively. If P is their point of intersection, then `S_1 P and S_2 P` are the roots of quadratic equation

A point P is taken on the right half of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 having its foci as S_1 and S_2 . If the internal angle bisector of the angle angleS_1PS_2 cuts the x-axis at poin Q(alpha, 0) then range of alpha is

A point P is taken on the right half of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 having its foci as S_1 and S_2 . If the internal angle bisector of the angle angleS_1PS_2 cuts the x-axis at poin Q(alpha, 0) then range of alpha is

Let P be a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 of eccentricity edot If A ,A ' are the vertices and S ,S are the foci of the ellipse, then find the ratio area P S S ' ' : area A P A^(prime)dot

Let P be a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 of eccentricity edot If A ,A ' are the vertices and S ,S are the foci of the ellipse, then find the ratio area P S S ' ' : area A P A^(prime)dot

Let P be a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 of eccentricity edot If A ,A ' are the vertices and S ,S are the foci of the ellipse, then find the ratio area P S S ' ' : area A P A^(prime)dot

Let P be a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 of eccentricity edot If A ,A ' are the vertices and S ,S are the foci of the ellipse, then find the ratio area P S S ' ' : area A P A^(prime)dot

A tangent is drawn at any point on the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 . If this tengent is intersected by the tangents at the vertices at points P and Q then show that S, S' , P and Q are concyclic points where S and S' are the foci of the hyperbola .