Question

Let P be a point of the parabola y² = 3(2x – 3) and M is the foot of perpendicular drawn from P on the directrix of the parabola, then length of each side of an equilateral triangle SMP, where S is focus of the parabola is 

(a)  6 

(b)  8 

(c)  10 

(d)  11 

Answer 1

Correct option   (a)  6 

Explanation:

Equation of parabola is

y² = 6(x - 3/2)

focus S(3,0) equation of directrix x = 0

P(3/2 + 3/2t² , 3t)

Coordinates of M (0,3t)

MS = √(9 + 9t²)

MP = 3/2 + 3/2 t^{2, But MS = MP}

9 + 9t² = 9/4t² + 9/4 t²

t² = 3

Length of side = 6 ​​​​​​​