`(b^2)/(sqrt(a^2+b^2)+a)`

Tangents are drawn to the ellipse from the point ((a^2)/(sqrt(a^2-b^2)),sqrt(a^2+b^2))) . Prove that the tangents intercept on the ordinate through the nearer focus a distance equal to the major axis.

Tangents are drawn to the ellipse from the point ((a^2)/(sqrt(a^2-b^2)),sqrt(a^2+b^2))) . Prove that the tangents intercept on the ordinate through the nearer focus a distance equal to the major axis.

Tangents are drawn to the ellipse from the point ((a^2)/(sqrt(a^2-b^2)),sqrt(a^2+b^2))) . Prove that the tangents intercept on the ordinate through the nearer focus a distance equal to the major axis.

If x = (sqrt(a^2+b^2)+sqrt(a^2-b^2))/(sqrt(a^2+b^2)-sqrt(a^2-b^2)) show that b^2x^2-2a^2x+b^2 =0 .

Given x = (sqrt(a^(2) + b^(2)) + sqrt(a^(2) - b^(2)))/(sqrt(a^(2) + b^(2)) - sqrt(a^(2) - b^(2))) . Use componendo and dividendo to prove that : b^(2) = (2a^(2)x)/(x^(2) + 1) .

Evaluate: int_sqrt((3a^2+b^2)/2)^sqrt((a^2+b^2)/2) (x*dx)/(sqrt((x^2-a^2)(b^2-x^2)))

Evaluate: int_sqrt((3a^2+b^2)/2)^sqrt((a^2+b^2)/2) (x*dx)/(sqrt((x^2-a^2)(b^2-x^2)))

If a and b are positive numbers such that a gt b , then the minimum value of a sec theta- b tan theta (0 lt theta lt pi/2) is a) 1/sqrt(a^2-b^2) b) 1/sqrt(a^2+b^2) c) sqrt(a^2+b^2) d) sqrt(a^2-b^2)

Tangents are drawn to the ellipse from the point ((a^(2))/(sqrt(a^(2)-b^(2))),sqrt(a^(2)+b^(2)))). Prove that the tangents intercept on the ordinate through the nearer focus a distance equal to the major axis.