MHT CET · Maths · Differential Equations
The differential equation of all circles having their centres on the line \(\mathrm{y}=5\) and touching X -axis is ......
- A \((5-\mathrm{y}) \frac{\mathrm{d} y}{\mathrm{~d} x}+\mathrm{y}^2-10 \mathrm{y}=0\)
- B \((5-\mathrm{y})^2 \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}+\mathrm{y}^2-10 \mathrm{y}=0\)
- C \((5-\mathrm{y}) \frac{\mathrm{dy}}{\mathrm{d} x}+\mathrm{y}-10=0\)
- D \((5-\mathrm{y})^2\left(\frac{\mathrm{dy}}{\mathrm{d} x}\right)^2+\mathrm{y}^2-10 \mathrm{y}=0\)
Answer & Solution
Correct Answer
(D) \((5-\mathrm{y})^2\left(\frac{\mathrm{dy}}{\mathrm{d} x}\right)^2+\mathrm{y}^2-10 \mathrm{y}=0\)
Step-by-step Solution
Detailed explanation
Equation of circle: \( (x-h)^2 + (y-5)^2 = 5^2 \) Differentiate w.r.t. \(x\): \( 2(x-h) + 2(y-5)\frac{dy}{dx} = 0 \)
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