Find the locus of points which is equidistant from P(4, 5) and Q(-6, -1).
A binary operation ,*, is defined on the set R, of real numbers by \(a * b = a^{2} + b + ab\). Find the value of x for which \(5 * x = 37\).
Find the derivative of \(3x^{2} + \frac{1}{x^{2}}\)
The coefficient of the 5th term in the binomial expansion of \((1 + kx)^{8}\), in ascending powers of x is \(\frac{35}{8}\). Find the value of the constant k.
Given that \(f '(x) = 3x^{2} - 6x + 1\) and f(3) = 5, find f(x).
