CUET · MATHS · PYQ PAPER 2025
If the slope of the tangent to the curve \(y=y(x)\) at any point \((x, y)\) is \(\frac{2 x}{y^2}\) and the curve passes through the point \(\left(\frac{1}{\sqrt{3}}, 1\right)\), then the equation of the curve is :
- A \(y^2=3 x^3\)
- B \(y^3=3 x^2\)
- C \(y^4=3 x^2\)
- D \(y=3 x^2\)
Answer & Solution
Correct Answer
(B) \(y^3=3 x^2\)
Step-by-step Solution
Detailed explanation
\(\frac{dy}{dx} = \frac{2x}{y^2}\) \(\int y^2 dy = \int 2x dx\) \(\frac{y^3}{3} = x^2 + C\) \(\frac{(1)^3}{3} = \left(\frac{1}{\sqrt{3}}\right)^2 + C \Rightarrow \frac{1}{3} = \frac{1}{3} + C \Rightarrow C=0\) \(\frac{y^3}{3} = x^2\) \(y^3 = 3x^2\)
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