The line y = x intersects the hyperbola `(x^(2))/(9) -(y^(2))/(25) = 1 ` at the points P and Q . The eccentricity of ellipse with PQ as major axis and minor axis of length `(5)/(sqrt(2))` is _

The line y=x intersects the hyperbola (x^(2))/(9)-(y^(2))/(25)=1 at the points P and Q. The eccentricity of ellipse with PQ axis and minor axis of length (5)/(sqrt(2)) is (A) (sqrt(5))/(3) (B) (5)/(sqrt(3))(C)(2(sqrt(2)))/(3)(D)(3)/(sqrt(2))

Let P be a point on the ellipse (x^(2))/(16) + (y^(2))/(9) = 1 . If the distance of P from centre of the ellipse be equal with the average value of semi major axis and semi minor axis, then the coordinates of P is _

In an ellipse, minor axis = 8 and eccentricity = sqrt(5)//3 then major axis =

The line 2x+y=1 is tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1. If this line passes through the point of intersection of the nearest directrix and the x-axis,then the eccentricity of the hyperbola is

Find the coordinates of foci, vertices, eccentricity, latus rectum and major and minor axis of the ellipse x^2/100+y^2/25=1 .

The line 2x + y = 1 is tangent to the hyperbola x^2/a^2-y^2/b^2=1 . If this line passes through the point of intersection of the nearest directrix and the x-axis, then the eccentricity of the hyperbola is