The number of values of $c$ such that line $y = cx + c$, $c \in R$ touches the curve $\frac{{{x^2}}}{4} + \frac{{{y^2}}}{1} = 1$ is

Consider the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$. Let $S(p, q)$ be a point in the tirst quadrant such that $\frac{p^2}{9}+\frac{q^2}{4}>1$. I wo tangents are drawn from $S$ to the ellipse, of which one meets the ellipse at one end point of the minor axis and the other meets the ellipse at a point $T$ in the fourth quadrant. Let $R$ be the vertex of the ellipse with positive $x$-coordinate and $O$ be the center of the ellipse. If the area of the triangle $\triangle O R T$ is $\frac{3}{2}$, then which of the following options is correct?

The number of $p$ oints which can be expressed in the form $(p_1/q_ 1 ,  p_2/q_2)$, ($p_i$ and $q_i$ $(i = 1,2)$ are co-primes) and lie on the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$ is

The equation of normal at the point $(0, 3)$ of the ellipse $9{x^2} + 5{y^2} = 45$ is

If $P \equiv (x,\;y)$, ${F_1} \equiv (3,\;0)$, ${F_2} \equiv ( – 3,\;0)$ and $16{x^2} + 25{y^2} = 400$, then $P{F_1} + P{F_2}$ equals