JEE Mains · Maths · STD 12 - 9. differential equations
If the differential equation representing the family of all circles touching \(x-\) axis at the origin is \(\left( {{x^2} - {y^2}} \right)\frac{{dy}}{{dx}} = g\left( x \right)y\) , then \(g(x)\) equals
- A \(\frac{1}{2}\,x\)
- B \(2x^2\)
- C \(2x\)
- D \(\frac{1}{2}\,x^2\)
Answer & Solution
Correct Answer
(C) \(2x\)
Step-by-step Solution
Detailed explanation
Since family of all circles touching \(x\) - axis at the origin \(\therefore \mathrm{Eqn}\) is \((x)^{2}+(y-a)^{2}=a^{2}\) where \((0, a)\) is the centre of circle \(\Rightarrow x^{2}+y^{2}+a^{2}-2 a y=a^{2}\) \(\Rightarrow x^{2}+y^{2}-2 a y=0\) ...\((1)\) Differentiate both…
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