COMEDK · Maths · 12. Circle
The value of \(k\) so that \(x^{2}+y^{2}+k x+4 y+2=0\) and \(2\left(x^{2}+y^{2}\right)-4 x-3 y+k=0\) cut orthogonally is
- A \(\frac{10}{3}\)
- B \(-\frac{8}{3}\)
- C \(-\frac{10}{3}\)
- D \(\frac{8}{3}\)
Answer & Solution
Correct Answer
(C) \(-\frac{10}{3}\)
Step-by-step Solution
Detailed explanation
Given, circles can be written as \[ x^{2}+y^{2}+k x+4 y+2=0 \] and \(x^{2}+y^{2}-2 x-\frac{3}{2} y+\frac{k}{2}=0\) Since, both circles are orthogonal, then \(2 g_{1} g_{2}+2 f_{1} f_{2}=c_{1}+c_{2}\) \(\Rightarrow \quad-k-3=2+\frac{k}{2}\) \(\frac{3 k}{2}=-5\)…
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