Find the angle between the lines , `(a^(2) - ab) y = (ab+b^(2))x+b^(3)` , and` (ab+b^(2)) y = (ab-a^2)x+a^(3)` where `a lt b lt 0`

Factorise a ^(3) - 3a^(2) b + 3ab ^(2) -b ^(3)

Angle between the lines (x)/( a) + (y)/( b) and (x)/(a) - (y)/( b) = 1 is ….....

If a,b,c are three terms in A.P and a^(2), b^(2), c^(2) are in G.P. and a + b + c = (3)/(2) then find a. (where a lt b lt c )

Show that the tangent of an angle between the lines (x)/(a) + (y)/( b) = 1 and (x)/( a) - (y)/( b) = 1 is (2 ab)/( a^(2) - b^(2) ) .

Find the sum of n terms of the series (a+b)+(a^(2)+ab+b^(2))+(a^(3)+a^(2)b+ab^(2)+b^(3))+"......." where a ne 1,bne 1 and a ne b .

Factorise each of the following : 64a^(3) - 27b^(3) - 144a^(2)b + 108ab^(2)

Find the product (2a + b+c) (4a ^(2) + b ^(2) + c ^(2) - 2ab -bc -2ca)

Find the slope of bar(AB) , where A(-4, 2), B(-4, -2)

Find the area bounded by the ellipse (x^2 )/( a^2) +(y^2)/(b^2) =1 and the cordinates x=0 and x = ae , where b^2 = a^2 ( 1- e^2) and e lt 1 .