AP EAMCET · Maths · Application of Derivatives
The two curves \(x=y^2, \quad x y=a^3 \quad\) cut orthogonally at a point, then \(a^2\) is equal to
- A \(\frac{1}{3}\)
- B \(\frac{1}{2}\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
We have, \[ x=y^2 \] \[ \Rightarrow \quad 2 y \frac{d y}{d x}=1 \Rightarrow \frac{d y}{d x}=\frac{1}{2 y} \] and \[ x y=a^3 \] \[ \Rightarrow \quad x \frac{d y}{d x}+y=0 \Rightarrow \frac{d y}{d x}=-\frac{y}{x} \] On solving equations (i) and (ii), we get the point of…
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