A differential equation representing the family of parabolas with axis parallel to y-axis …

Question

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 3x + 4y = 5, is given by :

Accepted Answer

Length of latus rectum

$$= {{|3(2) + 4( - 3) - 5|} \over 5} = {{11} \over 5}$$

$${(x - h)^2} = {{11} \over 5}(y - k)$$

differentiate w.r.t. 'x' :-

$$2(x - h) = {{11} \over 5}{{dy} \over {dx}}$$

again differentiate

$$2 = {{11} \over 5}{{{d^2}y} \over {d{x^2}}}$$

$${{11{d^2}y} \over {d{x^2}}} = 10$$

Solutions · 1