TS EAMCET · Maths · Application of Derivatives
If the curves \(y^2=12 x-3\) and \(y^2=12-k x\) cut each other orthogonally then the length of the sub tangent at \((1, b)\) on the curve \(y^2=12-k x\) is
- A \(4\)
- B \(6\)
- C \(5\)
- D \(12\)
Answer & Solution
Correct Answer
(B) \(6\)
Step-by-step Solution
Detailed explanation
\(m_1 = \frac{d}{dx}(12x-3) / (2y) = \frac{6}{y}\) \(m_2 = \frac{d}{dx}(12-kx) / (2y) = \frac{-k}{2y}\) \(m_1 m_2 = -1 \Rightarrow (\frac{6}{y})(\frac{-k}{2y}) = -1 \Rightarrow 3k = y^2\) \(y^2=12x-3\) and \(y^2=12-kx\)…
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