If $\theta$ is the acute angle between the lines $2x^2 + 7xy + 3y^2 = 0$, then the value of $\dfrac{2\cos\theta - 3\sin\theta}{4\sin\theta + 5\cos\theta} = \ldots$

The combined equation of the pair of lines passing through the origin and making an angle $\dfrac{\pi}{4}$ with the line $3x + y - 6 = 0$ is...

The number of lines passing through A (3, 4) and the sum of whose non-zero intercepts is zero is (are)

If $4ab = 3h^2$, then the ratio of the slopes of the lines represented by $ax^2 + 2hxy + by^2 = 0$ is...