A differential equation representing parabolas with axis parallel to the y-axis, whose lat…

Question

A differential equation representing parabolas with axis parallel to the $y$-axis, whose latus rectum equals the distance of $(2,-3)$ from $3x+4y=5$, is:

Accepted Answer

Distance $=\dfrac{|6-12-5|}{5}=\dfrac{11}{5}$; latus rectum $4a=\dfrac{11}{5}$. From $(x-h)^2=4a(y-k)$, differentiating twice gives $2=4a\dfrac{d^2y}{dx^2} \implies 11\dfrac{d^2y}{dx^2}=10$.

Solutions · 1