Question

solve this without spamming :)​

Answer 1

Answer:

$\bold\red{(D)\frac{4( \sqrt{3} + 2) }{3} }$

Step-by-step explanation:

Given,

$y - \sqrt{3} x + 3 = 0$

We can also write it as,

$\frac{y - 0}{ \frac{ \sqrt{3} }{2} } = \frac{x - \sqrt{3} }{ \frac{1}{2} } = r \: \: \: \: \: \: ...........(i)$

Substituting,

$x = \sqrt{3} + \frac{r}{2}$

and,

$y = \frac{ \sqrt{3} }{2} r$

in the parabola,

${y}^{2} = x + 2$

we get,

$= > \frac{3 {r}^{2} }{4} = \frac{r}{2} + \sqrt{3} + 2 \\ \\ = > 3 {r}^{2} - 2r - (4 \sqrt{3} + 8) = 0$

Therefore,

we get,

$= > PA .PB = |r1.r2| = \frac{4 \sqrt{3} + 8 }{3} \\ \\ = > PA.PB</p><p> = \frac{4( \sqrt{3} + 2) }{3} </p><p>$

Hence,

Correct Option is (D)