JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let a circle \(C:(x-h)^{2}+(y-k)^{2}=r^{2}, k>0\), touch the \(x\)-axis at \((1,0)\). If the line \(x + y =0\) intersects the circle \(C\) at \(P\) and \(Q\) such that the length of the chord \(PQ\) is \(2\) , then the value of \(h + k + r\) is equal to
- A \(6\)
- B \(15\)
- C \(9\)
- D \(7\)
Answer & Solution
Correct Answer
(D) \(7\)
Step-by-step Solution
Detailed explanation
\(k = r\) \(h =1\) \(OP = r , PR =1\) \(OR =\left|\frac{ r +1}{\sqrt{2}}\right|\) \(r ^{2}=1+\frac{( r +1)^{2}}{2}\) \(2 r ^{2}=2+ r ^{2}+1+2 r\) \(r ^{2}-2 r -3=0\) \(( r -3)( r +1)=0\) \(r =3,-1\) \(h + k + r =1+3+3\) \(=7\)
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