Prove that the straight lines `x/a-y/b =m and x/a+y/b=1/m,` where `a and b` are given positive real numbers and `'m'` is a parameter, always meet on a hyperbola.

Given that x,y and b real are real numbers and x ge y , b gt 0 , then

The locus of point of intersection of the lines x/a-y/b=m and x/a+y/b=1/m (i) a circle (ii) an ellipse (iii) a hyperbola (iv) a parabola

Prove that (x/a)^n+(y/b)^n=2 touches the straight line x/a+y/b=2 for all n in N , at the point (a ,\ b) .

If (x-a)^(2m) (x-b)^(2n+1) , where m and n are positive integers and a > b , is the derivative of a function f then-

If (x-a)^(2m) (x-b)^(2n+1) , where m and n are positive integers and a > b , is the derivative of a function f then-

Given that x , y and b are real numbers and x le y, b lt 0 then

(i) Find the eccentricity of hyperbola whose latus rectum is half of its transverse axis. (ii) Prove that the straight lines (x)/(a)-(y)/(b)=mand(x)/(a)-(y)/(b)=(1)/(m) always meet at a hyperbola, where 'm' is a constant.

A variable straight line is drawn through the point of intersection of the straight lines x/a+y/b=1 and x/b+y/a=1 and meets the coordinate axes at A and Bdot Show that the locus of the midpoint of A B is the curve 2x y(a+b)=a b(x+y)

Let a, x, b in A.P, a, y, b in GP a, z, b in HP where a and b are disnict positive real numbers. If x = y + 2 and a = 5z , then which of the following is/are COR RECT ?

if m and b are real numbers and mbgt0 , then the line whose equation is y=mx+b cannot contain the point