TS EAMCET · Maths · Application of Derivatives
If \(y=2 x\) is a tangent to the curve \(y^2=a x^3+b\) at \((1,2)\), then \((a, b)=\)
- A \((8,4)\)
- B \(\left(\frac{2}{3}, 1\right)\)
- C \(\left(\frac{8}{3}, \frac{4}{3}\right)\)
- D \(\left(\frac{8}{3}, \frac{2}{3}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{8}{3}, \frac{4}{3}\right)\)
Step-by-step Solution
Detailed explanation
We have, \[ y^2=a x^3+b \] Differentiate w.r.t ' \(x\) ' \[ \begin{gathered} 2 y \frac{d y}{d x}=3 a x^2 \\ \frac{d y}{d x}=\frac{3 a x^2}{2 y} \end{gathered} \] Slope at \((1,2)\)…
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