Show thathte coefficients of `x^(2),xy and y^(2) "in" ax^(2)+2hxy+by^(2)` are invariants under the translatio of axes.

y^(2) = 4ax

y= ax + bx^(2)

If the coefficients of x^(2) and x^(11) in the expansion of (1+ax+2x^(2))^(6) be 27 and (-192) respectively , show that , a=-1

Find the differential coefficient of: tan^(2)(ax)

If the magnitude of the coefficient of x^(7) in the expansion of (ax^(2)+(1)/(bx))^(8) , where a, b are positive numbers, is equal to the magnitude of the coefficient of x^(-7) in the expansion of (ax-(1)/(bx^(2)))^(8) , then a and b are connected by the relation

If the sum of the coefficients of the expansion (a^(2)x^(2)-2ax+1)^(51) be zero , than the value of a will be -

The sum of the coefficient in the expansion of (1+ax-2x^(2))^(n) is

y = (ax + b) e^(-2x)

Reduce the equation 5x^(2)-2y^(2)-30x+8y=0 to the form ax^(2)+by^(2)=1 by proper translation of axes without rotation .

The condition that one of the straight lines given by the equation ax^(2)+2hxy+by^(2)=0 may coincide with one of those given by the equation a'x^(2)+2h'xy+b'y^(2)=0 is