" (ix) "(b^(2))/(sqrt(a^(2)+b^(2))+a)

Express each one of the following with rational denominator: (3sqrt(2)+1)/(2sqrt(5)-3) (ii) (b^(2))/(sqrt(a^(2)+b^(2))+a)

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) .

Rationalize the denominator of each of the following expressions : ( 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.

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

The value of (a+sqrt((a)-b^(2)))/(a-sqrt(a^(2)-b^(2)))+(a-sqrt(a^(2)-b^(2)))/(a+sqrt(a^(2)-b^(2)) is

(sqrt(a^(2)-b^(2))+a)/(sqrt(a^(2)+b^(2))+b)-:(sqrt(a^(2)+b^(2))-b)/(a-sqrt(a^(2)-b^(2)))

Express each one of the following with rational denominator: (i) (3sqrt(2)+\ 1)/(2sqrt(5)-3) (ii) (b^2)/(sqrt(a^2+b^2)+\ a)

u=sqrt(a^(2)cos^(2)theta+b^(2)sin^(2)theta)+sqrt(a^(2)sin^(2)theta+b^(2)cos^(2)theta^(2)) then the difference between the maximum and minimum values of u^(2) is given by : (a) (a-b)^(2) (b) 2sqrt(a^(2)+b^(2))(c)(a+b)^(2) (d) 2(a^(2)+b^(2))

Equation of a normal to the given ellipse whose slope is 'm' is y=ma-+((a^(2)-b^(2))m)/(sqrt(a^(2)+b^(2)m^(2)))