CUET · MATHS · PYQ PAPER 2023
The points on the curve \(\frac{x^2}{16}+\frac{y^2}{25}=1\) at which tangents are parallel to \(x\)-axis are:
- A \(( \pm 5,0)\)
- B \(( \pm 4,0)\)
- C \((0, \pm 5)\)
- D \((0, \pm 4)\)
Answer & Solution
Correct Answer
(C) \((0, \pm 5)\)
Step-by-step Solution
Detailed explanation
\(\frac{x^2}{16}+\frac{y^2}{25}=1 \implies \frac{x}{8} + \frac{2y}{25} \frac{dy}{dx} = 0 \implies \frac{dy}{dx} = -\frac{25x}{16y}\) Tangent parallel to \(x\)-axis \(\implies \frac{dy}{dx}=0 \implies x=0\) Substitute \(x=0\):…
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