(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) .

(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

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.

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

If (1+i)(1+2i)(1+3i)......(1+ni)=a+ib,then2xx5xx10...(1+n^(2)) is equal to sqrt(a^(2)+b^(2))(b)sqrt(a^(2)-b^(2))(c)a^(2)+b^(2)(d)a^(2)-b^(2)(e)a+b

The distance between the points (a cos theta+b sin theta,0) and (0,a sin theta-b cos theta) is a^(2)+b^(2)(b)a+ba^(2)-b^(2)(d)sqrt(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)))

Distance of the points (a,b,c) for the y axis is (a) sqrt(b^(2)+c^(2)) (b) sqrt(c^(2)+a^(2)) (c )sqrt(a^(2)+b^(2)) (d) sqrt(a^(2)+b^(2)+c^(2))

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