Question

 Find the position (interior or exterior or on) of the following points with respect to the parabola y² = 6x. (i) (6, –6), (ii) (0, 1), (iii) (2, 3) 

Answer 1

Equation of the parabola is y² = 6x 

⇒S ≡ y²– 6x 

i) S₁₁ = (–6)² – 6.6 = 36 – 36 = 0 

∴ (6, –6) lies on the parabola. 

ii) (0, 1) 

S₁₁ = 1² – 6.0 = 1 > 0 

∴ (0, 1) lies outside the parabola. 

iii)(2, 3) 

S₁₁ = 3² – 6.2 = 9 – 12 = –3 < 0 

∴ (2, 3) lies inside the parabola.