AP EAMCET · Maths · Application of Derivatives
Find the area of the triangle formed by the \(X\)-axis and the tangent and the normal to the curve \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) at the point \(\left(\frac{a}{\sqrt{2}}, \frac{b}{\sqrt{2}}\right)\)
- A \(\frac{a b}{4} \sqrt{a^2+b^2}\)
- B \(4 a b\)
- C \(\frac{b}{4 a}\left(a^2+b^2\right)\)
- D \(\frac{a b}{2} \sqrt{a^2+b^2}\)
Answer & Solution
Correct Answer
(C) \(\frac{b}{4 a}\left(a^2+b^2\right)\)
Step-by-step Solution
Detailed explanation
Ellipse, \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1...(i)\) To find Equation of tangent and normal at point \(\left(\frac{a}{\sqrt{2}}, \frac{b}{\sqrt{2}}\right)\) We have to find \(\frac{d y}{d x}\). Slope of tangent…
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