Question

ax^2+2hxy+by^2=1 prove that d^2y/dx^2=h^2-ab/(hx+by)^3

Answer 1

You need to find the value of 'y' in terms of 'x'
Take the given expression as quadratic equation in 'y' and find the values of 'y'
Study differentiability then derive twice
And that should prove it.
P.S. This may not be the best method though