Question

Find the equation of the parabola whose latus rectum is 4 units, axis is the line \( 3 x+4 y=4 \) and the tangent at the vertex is the line \( 4 x-3 y+7=0 \).

Answer 1

Given latus rectum of the parabola is, 4a = 4

⇒ a = 1

also axis is Y = 3x+4y−4 = 0 and tangent at the vertex is X = 4x−3y+7 = 0

So the required parabola is Y² = 4aX

⇒(3x+4y−4)² = 4(4x−3y+7)