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A differential equation representing the family of parabolas with axis parallel to \(y-\)axis and whose length of latus …

Q1

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 :

[JEE Main 2021, 27 Aug (Shift 2)]

a

\(10\frac{{\mathrm{d}}^{2}\mathrm{x}}{{\mathrm{dy}}^{2}}=11\)

b

\(11\frac{{\mathrm{d}}^{2}\mathrm{y}}{{\mathrm{dx}}^{2}}=10\)

c

\(11\frac{{\mathrm{d}}^{2}\mathrm{x}}{{\mathrm{dy}}^{2}}=10\)

d

\(10\frac{{\mathrm{d}}^{2}\mathrm{y}}{{\mathrm{dx}}^{2}}=11\)

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