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  • A differential equation representing the family of parabolas with axis parallel to and whose length of latus rectum is the distance of the point <img alt="(2,-3)" src="https:/

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) form the line 3 x+4 y=5, is given by :
Option: 1 11 \frac{\mathrm{d}^{2} x}{\mathrm{~d} y^{2}}=10
Option: 2 11 \frac{\mathrm{d}^{2} x}{\mathrm{~d} y^{2}}=10
Option: 3 11 \frac{\mathrm{d}^{2} x}{\mathrm{~d} y^{2}}=10
Option: 4 11 \frac{\mathrm{d}^{2} x}{\mathrm{~d} y^{2}}=10
Option: 5 10 \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=11
Option: 6 10 \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=11
Option: 7 10 \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=11
Option: 8 10 \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=11
Option: 9 11 \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=10
Option: 10 11 \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=10
Option: 11 11 \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=10
Option: 12 11 \frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}=10
Option: 13 10 \frac{\mathrm{d}^{2} x}{\mathrm{~d} y^{2}}=11
Option: 14 10 \frac{\mathrm{d}^{2} x}{\mathrm{~d} y^{2}}=11
Option: 15 10 \frac{\mathrm{d}^{2} x}{\mathrm{~d} y^{2}}=11
Option: 16 10 \frac{\mathrm{d}^{2} x}{\mathrm{~d} y^{2}}=11

Answers (1)

best_answer

LR= \left | \frac{3\times 2+4\left ( -3 \right )-5}{\sqrt{3^{2}+4^{2}}} \right |= \frac{11}{5}

Let the vertex is \left ( \alpha ,\beta \right )

Equation of Parabola is

      \left ( x-\alpha \right )^{2}= \frac{11}{5}\left ( y-\alpha \right )\\

\Rightarrow 2\left ( x-\alpha \right )= \frac{11}{5}\frac{dy}{dx}\\

\Rightarrow 2= \frac{11}{5}\frac{d^{2}y}{dx^{2}}\\

\Rightarrow 11\frac{d^{2}y}{dx^{2}}= 10

Posted by

Kuldeep Maurya

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