JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let a circle \(C\) of radius \(5\) lie below the \(x\)-axis. The line \(L_{1}=4 x+3 y-2\) passes through the centre \(P\) of the circle \(C\) and intersects the line \(L _{2}: 3 x -4 y -11=0\) at \(Q\). The line \(L _{2}\) touches \(C\) at the point \(Q\). Then the distance of \(P\) from the line \(5 x-12 y+51=0\) is
- A \(9\)
- B \(10\)
- C \(11\)
- D \(12\)
Answer & Solution
Correct Answer
(C) \(11\)
Step-by-step Solution
Detailed explanation
\(4 x+3 y+2=0\) \(3 x-4 y-11=0\) \(\frac{x}{-25}=\frac{y}{50}=\frac{1}{-25}\) \(\frac{x-1}{\cos \theta}=\frac{y+2}{\sin \theta}=\pm 5\) \(y=-2+5\left(-\frac{4}{5}\right)=-6\) \(x=1+5\left(\frac{3}{5}\right)=4\) Req. distance \(\left|\frac{5(4)-12(-6)+51}{13}\right|\)…
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