Question

Find the equation of the parabola whose focus is (–2, 3) and directrix is the line 2x + 3y – 4 = 0. Also find the length of the latus rectum and the equation of the axis of the parabola.

Answer 1

Focus S(–2, 3) 

Equation of the directrix is 2x + 3y – 4 = 0. 

Let P(x₁, y₁) be any point on the parabola. 

SP² = (x₁ + 2)² + (y₁ – 3)² 

Let PM be the perpendicular from P to the directrix.

–6 – 6 + k = 0 ⇒ k = 12 

Equation of the axis is : 3x – 2y + 12 = 0