AP EAMCET · Maths · Application of Derivatives
If the curves \(y^2=16 x\) and \(9 x^2+\alpha y^2=25\) intersect at right angles, then \(\alpha=\)
- A 6
- B 9
- C \(\frac{9}{2}\)
- D 3
Answer & Solution
Correct Answer
(C) \(\frac{9}{2}\)
Step-by-step Solution
Detailed explanation
\(m_1 = \frac{d}{dx}(y^2=16x) = \frac{8}{y}\) \(m_2 = \frac{d}{dx}(9x^2+\alpha y^2=25) = \frac{-9x}{\alpha y}\) \(m_1 m_2 = -1 \Rightarrow \left(\frac{8}{y}\right) \left(\frac{-9x}{\alpha y}\right) = -1\) \(-72x = -\alpha y^2 \Rightarrow 72x = \alpha y^2\) \(72x = \alpha (16x)\)…
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