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`

Find the area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 .

P and Q are two points on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 whose eccentric angles are differ by 90^(@) , then

If P(alpha,beta) is a point on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with foci Sa n dS ' and eccentricity e , then prove that the area of S P S ' is basqrt(a^2-alpha^2)

If the normal at P(2,(3sqrt(3))/2) meets the major axis of ellipse (x^2)/(16)+(y^2)/9=1 at Q , and S and S ' are the foci of the given ellipse, then find the ratio S Q : S^(prime)Qdot

Let S and S'' be the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose eccentricity is i.e. P is a variable point on the ellipse. Consider the locus of the incenter of DeltaPSS'' The maximum area of recatangle inscribed in the locus is

P is a variable on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with AA' as the major axis. Find the maximum area of triangle A P A '

Let S and S' be the fociof the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose eccentricity is e. P is a variable point on the ellipse. Consider the locus the incenter of DeltaPSS' The eccentricity of the locus of the P is

Let S and S' be the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose eccentricity is e. P is a variable point on the ellipse. Consider the locus the incentre of DeltaPSS' . The locus of the incenter is a\an

P and Q are the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and B is an end of the minor axis. If P B Q is an equilateral triangle, then the eccentricity of the ellipse is

If e_1 is the eccentricity of the ellipse x^2/16+y^2/25=1 and e_2 is the eccentricity of the hyperbola passing through the foci of the ellipse and e_1 e_2=1 , then equation of the hyperbola is