A differential equation representing the family of parabolas with axis parallel to y - axis and whose length of latus rectum is the distance of the point ( 2 , - 3 ) from the line 3 x + 4 y = 5 , is given by:

Step-by-step solution

The equation of family of parabolas ( x - α ) 2 = 4 a ( y - β ) Distance of point ( 2 , - 3 ) from line 3 x + 4 y = 5 is 4 a = 3 × 2 + 4 × - 3 − 5 5 4 a = 6 − 12 − 5 5 4 a = 11 5 ( x − α ) 2 = 11 5 ( y − β ) Differentiate w.r.t. x 2 ( x − α ) = 11 5 d y d x Again diff. w. r. t. x 2 = 11 5 d 2 y d x 2 11 d 2 y d x 2 = 10