CUET · MATHS · PYQ PAPER 2025
The number of tangents to the curve \(x y-3 y+2=0\) having slope 2 is :
- A 0
- B 1
- C 2
- D Infinite
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
Differentiate implicitly: \( x \frac{dy}{dx} + y - 3 \frac{dy}{dx} = 0 \implies \frac{dy}{dx} = \frac{y}{3-x} \) Set \(\frac{dy}{dx} = 2\): \( \frac{y}{3-x} = 2 \implies y = 2(3-x) \) Substitute \(y\) into original equation: \( x(2(3-x)) - 3(2(3-x)) + 2 = 0 \) Simplify:…
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