If `a x^2+2h x y+b y^2=1,t h e n(d^(2y))/(dx^2)` is `(h^2-a b)/((h x+b y)^2)` (b) `(a b-h^2)/((h x+b y)^2)` `(h^2+a b)/((h x+b y)^2)` (d) none of these

Options

A. `(h^(2)-ab)/((hx+by)^(3))`
B. `(ab-h^(2))/(hx+by)^(2)`
C. `(h^(2)+ab)/(hx+by)^(2)`
D. none of these

Explanation

To find \(\frac{d^2y}{dx^2}\) given the equation \(ax^2 + 2hxy + by^2 = 1\), we will differentiate the equation twice with respect to \(x\).

### Step 1: Differentiate the equation with respect to \(x\)

Starting with the equation:
\[ ax^2 + 2hxy + by^2 = 1 \]
...