TS EAMCET · Maths · Application of Derivatives
If the tangent and the normal drawn to the curve \(x y^2+x^2 y=12\) at the point \((1,3)\) meet the X -axis in T and N respectively, then \(\mathrm{TN}=\)
- A \(\frac{7}{5}\)
- B \(\frac{45}{7}\)
- C \(\frac{3 \sqrt{274}}{7}\)
- D \(\frac{274}{35}\)
Answer & Solution
Correct Answer
(D) \(\frac{274}{35}\)
Step-by-step Solution
Detailed explanation
\(\frac{d}{dx}(xy^2+x^2y) = \frac{d}{dx}(12)\) \(y^2+2xy\frac{dy}{dx}+2xy+x^2\frac{dy}{dx}=0\) \(\frac{dy}{dx} = -\frac{y^2+2xy}{x^2+2xy}\) \(m_t = \frac{dy}{dx}\bigg|_{(1,3)} = -\frac{3^2+2(1)(3)}{1^2+2(1)(3)} = -\frac{9+6}{1+6} = -\frac{15}{7}\) Tangent:…
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