CUET · MATHS · PYQ PAPER 2023
The slope of the normal to the curve \(x^2+3 y+y^2=5\) at \((1,1)\) is :
- A \(\frac{5}{2}\)
- B \(\frac{2}{5}\)
- C \(-\frac{2}{5}\)
- D \(-\frac{5}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{5}{2}\)
Step-by-step Solution
Detailed explanation
\( \frac{d}{dx}(x^2+3y+y^2) = \frac{d}{dx}(5) \) \( 2x + 3\frac{dy}{dx} + 2y\frac{dy}{dx} = 0 \) \( \frac{dy}{dx} = \frac{-2x}{3+2y} \) \( m_t = \frac{-2(1)}{3+2(1)} = -\frac{2}{5} \) \( m_{normal} = -\frac{1}{m_t} = -\frac{1}{(-2/5)} = \frac{5}{2} \)
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