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Find the differential equation of the family of circles whose centres lie on `X`-axis.A. `(d^(2)y)/(dx^(2)) + ((dy)/(dx))^(2) + 1 = 0`B. `y""(d^(2)y)/(dx^(2)) + ((dy)/(dx))^(2) - 1 = 0`C. `y""(d^(2)y)/(dx^(2)) - ((dy)/(dx))^(2) - 1 = 0`D. `y""(d^(2)y)/(dx^(2)) + ((dy)/(dx))^(2) + 1 = 0` |
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Answer» Correct Answer - D The equation of family of circle having centre at x-axis is `x^(2) + y^(2) - 2ax = 0` On differentiating , we get `2x + 2y""(dy)/(dx) - 2a = 0` Again , differentiating , we get `2 + 2 [y ""(d^(2) y)/(dx^2) + ((dy)/(dx))^(2)]`= 0 `iimplies y""(d^(2)y)/(dx^(2)) + ((dy)/(dx))^(2) + 1 = 0` |
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