AP EAMCET · Maths · Ellipse
If \(\mathrm{P}(\alpha, \beta)\) is a point on the curve \(9 \mathrm{x}^2+4 \mathrm{y}^2=144\) in the first quadrant and the minimum area of the triangle formed by the tangent of the curve at \(P\) with the coordinate axis is S, then
- A \(s=\sqrt{\alpha \beta}\)
- B \(\mathrm{S}=\alpha \beta\)
- C \(S=2 \sqrt{\alpha \beta}\)
- D \(\mathrm{S}=2 \alpha \beta\)
Answer & Solution
Correct Answer
(D) \(\mathrm{S}=2 \alpha \beta\)
Step-by-step Solution
Detailed explanation
Equation of curve: \(9x^2 + 4y^2 = 144 \implies \frac{x^2}{16} + \frac{y^2}{36} = 1\). Tangent at \(P(\alpha, \beta)\): \(\frac{x\alpha}{16} + \frac{y\beta}{36} = 1\). Intercepts: \(x_0 = \frac{16}{\alpha}\), \(y_0 = \frac{36}{\beta}\). Area of triangle:…
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