AP EAMCET · Maths · Circle
If the circles \(x^2+y^2-2 x+4 y+c=0\) and \(x^2+y^2+2 x-\) \(4 y+c=0\) have four common tangents, then
- A \(\mathrm{c} < 0\)
- B \(-2 < \) c \( < 2\)
- C \(0 < \) c \( < 5\)
- D \(\mathrm{c}>0\)
Answer & Solution
Correct Answer
(C) \(0 < \) c \( < 5\)
Step-by-step Solution
Detailed explanation
The given equation of circle is as follows :- \(x^2+y^2-2 x+4 y+c=0\) ...(i) \(x^2+y^2+2 x-4 y+c=0\) ...(ii) Radius and centre of circle (i) is \(r_1=\sqrt{(-1)^2+(2)^2-c}=\sqrt{5-c}\) and \(c_1=(+1,-2)\) Radius and centre of circle (ii) is…
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