MHT CET · Maths · Circle
If the points \((2,0),(0,1),(4,5)\) and \((0, c)\) are concyclic, then the value of \(c\) is
- A 1
- B \(\frac{14}{3}\)
- C 5
- D None of these
Answer & Solution
Correct Answer
(B) \(\frac{14}{3}\)
Step-by-step Solution
Detailed explanation
The equation of the circle passing through \((2,0),(0,1)\) and \((4,5)\) is
\(
3\left(x^{2}+y^{2}\right)-13 x-17 y+14=0
\)
This passes through \((0, c)\).
\(\therefore 3 c^{2}-17 c+14=0\)
\(\Rightarrow c=1, \frac{14}{3}\)
Since, \(c=1\) is already there, for point \((0,1)\). Therefore, we take \(c=\frac{14}{3}\).
\(
3\left(x^{2}+y^{2}\right)-13 x-17 y+14=0
\)
This passes through \((0, c)\).
\(\therefore 3 c^{2}-17 c+14=0\)
\(\Rightarrow c=1, \frac{14}{3}\)
Since, \(c=1\) is already there, for point \((0,1)\). Therefore, we take \(c=\frac{14}{3}\).
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