A differential equation representing


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

  1. $10 \frac{d^{2} y}{d x^{2}}=11$

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

  3. $10 \frac{\mathrm{d}^{2} \mathrm{x}}{\mathrm{dy}^{2}}=11$

  4. $11 \frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}=10$

Correct Option: , 4


$\alpha . R=\frac{|3(2)+4(-3)-5|}{5}=\frac{11}{5}$


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

$2(x-h)=\frac{11}{5} \frac{d y}{d x}$

again differentiate

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

$\frac{11 \mathrm{~d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}=10$

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