CUET · MATHS · PYQ PAPER 2023
The points on the curve \(\frac{x^2}{9} + \frac{y^2}{16} = 1\) at which the tangents are parallel to x-axis :
- A \((0, 4), (0, -4)\)
- B \((0, 0), (0, -4)\)
- C \((4, 0), (-4, 0)\)
- D \((0, 0), (0, 4)\)
Answer & Solution
Correct Answer
(A) \((0, 4), (0, -4)\)
Step-by-step Solution
Detailed explanation
\(\frac{d}{dx}\left(\frac{x^2}{9} + \frac{y^2}{16}\right) = \frac{d}{dx}(1)\) \(\frac{2x}{9} + \frac{2y}{16}\frac{dy}{dx} = 0\) \(\frac{dy}{dx} = -\frac{8x}{9y}\) Set \(\frac{dy}{dx} = 0 \Rightarrow x = 0\) Substitute \(x=0\) into \(\frac{x^2}{9} + \frac{y^2}{16} = 1\):…
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