The equation of the normal to the curve $2x^{2} + 3y^{2} - 5 = 0$ at the point $P(1, 1)$ is:

If the tangent at point $(1, 2)$ on the curve $y = ax^2 + bx + \frac{7}{2}$ is parallel to the normal at $(-2, 2)$ on the curve $y = x^2 + 6x + 10$,then:

For the curve $\frac{x^n}{a^n}+\frac{y^n}{b^n}=2, (n \in N \text{ and } n > 1)$, the line $\frac{x}{a}+\frac{y}{b}=2$ is

The sum of the lengths of the subtangent and the subnormal drawn at $\theta = \frac{\pi}{3}$ on the cycloid $x = a(\theta - \sin \theta)$,$y = a(1 - \cos \theta)$ is

$f(x)$ is a continuous function on $\mathbb{R}$ and $y=f(x)$ is a curve. If $(\alpha, \beta)$ is a point such that $\beta=f(\alpha)$ and $p\alpha+m\beta+n=0$ $(p \neq 0, m \neq 0)$,then which one of the following is true?

The length of the subtangent at any point $(x_1, y_1)$ on the curve $y=5^x$ is