Find the equation of the parabola whose latus-rectum is `4u n i t s` , axis is the line `3x+4y-4=0` and the tangent at the vertex is the line `4x-3+7=0.`

Explanation

Given latus rectum of the parabola is, `4 a=4 Rightarrow a=1`


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


So the required parabola is `Y^{2}=4 {aX}`


`Rightarrow(3 x+4 y-4)^{2}=4(4 x-3 y+7)`