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Question
Choose the correct option from the given alternatives:
The differential equation of all circles having their centres on the line y = 5 and touching the X-axis is
Options
`"y"^2 (1 + "dy"/"dx") = 25`
`("y - 5")^2 [1 + ("dy"/"dx")^2] = 25`
`("y - 5")^2 + [1 + ("dy"/"dx")^2] = 25`
`("y - 5")^2 [1 - ("dy"/"dx")^2] = 25`
Solution
`("y - 5")^2 [1 + ("dy"/"dx")^2] = 25`
Hint: Equation of the circle is
(x - h)2 + (y - 5)2 = 52 ....(1)
∴ 2(x - h) + 2(y - 5)`"dy"/"dx" = 0`
∴ (x - h)2 = (y - 5)2 `("dy"/"dx")^2`
∴ 25 - (y - 5)2 = (y - 5)2 `("dy"/"dx")^2` ...[By (1)]
∴ (y - 5)2 `[1 + ("dy"/"dx")^2] = 25`
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