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15/01/2022 4:15 pm
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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
(1) \(10\frac{d^2y}{dx^2}\) = 11
(2) \(11\frac{d^2x}{dy^2}\) = 10
(3) \(10\frac{d^2x}{dy^2}\) = 11
(4) \(11\frac{d^2y}{dx^2}\) = 10
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15/01/2022 4:20 pm
Correct answer: (4) \(11\frac{d^2y}{dx^2}\) = 10
Explanation:
α.R = \(\frac{|3(2) + 4(-3)-5|}{5}\) = \(\frac{11}{5}\)
(x - h)2 = \(\frac{11}{5}\)(y - k)
differentiate w.r.t 'x' :
2(x - h) = \(\frac{11}{5}\)\(\frac{dy}{dx}\)
again differentiate
2 = \(\frac{11}{5}\)\(\frac{d^2y}{dx^2}\)
\(11\frac{d^2y}{dx^2}\) = 10