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

Question

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

Neha Sethi · Accepted Answer

Dear student
Kindly follow the another and easy approach of doing the
question

Let Px,y be any point on the parabola
Draw PN ⊥ to its axis and PM ⊥ to the tangent at the vertex
Theny2=4ax⇒PM2=Latus ractum×PN⇒PM2=Latus rectum×PN  
1      Because latus rectum of y2=4ax is 4aNow,PM=3x+4y-49+16    as distance of a point from directrix is : 3x+4y-432+42⇒PM=3x+4y-45PN=lenght of ⊥ from Px,y on the tangent at the vertex A⇒PN=4x-3y+716+9⇒PN=4x-3y+75Latus rectum=4 givenFrom 13x+4y-452=44x-3y+75or 3x+4y-42=204x-3y+7is the required eq of parabola
Regards