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JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let a point \(P\) be such that its distance from the point \((5,0)\) is thrice the distance of \(P\) from the point \((-5,0) .\) If the locus of the point \(P\) is a circle of radius \(r\), then \(4 r ^{2}\) is equal to ...... .
- A \(56\)
- B \(42\)
- C \(64\)
- D \(48\)
Answer & Solution
Correct Answer
(A) \(56\)
Step-by-step Solution
Detailed explanation
Let point is \(( h , k )\) So, \(\sqrt{( h -5)^{2}+ k ^{2}}=3 \sqrt{( h +5)^{2}+ k ^{2}}\) \(8 x^{2}+8 y^{2}+100 x+200=0\) \(x^{2}+y^{2}+\frac{25}{2} x+25=0\) \(r^{2}=\frac{(25)^{2}}{4^{2}}-25\) \(4 r^{2}=\frac{25^{2}}{4}-100\) \(4 r^{2}=156.25-100\) \(4 r^{2}=56.25\) After…
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