AP EAMCET · Maths · Application of Derivatives
The acute angle between the curves \(x^2+y^2=x+y\) and \(x^2+y^2=2 y\) is
- A \(\frac{2 \pi}{3}\)
- B \(\frac{\pi}{2}\)
- C \(\frac{\pi}{3}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(x^2+y^2=x+y\) \(\qquad ....\mathrm{(i)}\) \(x^2+y^2=2 y\) \(\qquad ....\mathrm{(ii)}\) Add (i) and (ii), \(2 x^2+2 y^2-3 y-x=0\) \(\qquad ....\mathrm{(iii)}\) Subtract (i) from (ii), \(x+y=0\) \(\qquad ....\mathrm{(iv)}\) Differentiate (i) w.r.t.…
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