question_answer

Equation of a straight line meeting the circle\[{{x}^{2}}+{{y}^{2}}=100\] in two points, each point at a distance of 4 from the point (8, 6) on the circle, is:

A) \[4x+3y-50=0\]

B) \[4x+3y-100=0\]

C) \[4x+3y-46=0\]

D) none of these

Correct Answer: C

Solution :

\[{{S}_{1}}:\]\[{{x}^{2}}+{{y}^{2}}=100\]

equation of \[{{S}_{2}}\] centred at (8, 6) is

\[{{(x-8)}^{2}}+{{(y-6)}^{2}}=16\]

\[{{x}^{2}}+{{y}^{2}}-16x-12y+84=0\]

\[\therefore \]      required line AB, (i.e. common chord)

\[{{S}_{1}}-{{S}_{2}}=0\]

\[\Rightarrow \]   \[{{x}^{2}}+{{y}^{2}}-16x-12y+84-{{x}^{2}}-{{y}^{2}}+100=0\]

\[-16x-12y+184=0\]

\[4x+3y-46=0\]