List of top Mathematics Questions on Tangents and Normals asked in AIEEE

An equation of a common tangent to the parabola $y^{2} = 16\sqrt{3}x$ and the ellipse $2x^{2} + y^{2} = 4$ is $y = 2x + 2\sqrt{3}$ If the line $y = mx + \frac{4\sqrt{3}}{m}, \left(m\ne0\right)$ is a common tangent to the parabola $y^{2} = 16\sqrt{3}x$ and the ellipse $2x^{2} + y^{2} = 4$, then m satisfies $m^{4} + 2m^{2} = 24.$

The normal to the curve $x=a\left(cos\,\theta+\theta\,sin\,\theta \right). y=a\left(sin\,\theta -\theta\,cos\,\theta \right)$ at any point $'\theta'$ is such that :