AP EAMCET · Maths · Circle
If \((a, b)\) is the midpoint of the chord \(2 x-y+3=0\) of the circle \(x^2+y^2+6 x-4 y+4=0\), then \(2 a+3 b=\)
- A -1
- B 0
- C 1
- D 3
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } 2 x-y+3=0, \Rightarrow y=2 x+3 \\ & x^2+y^2+6 x-4 y+4=0 \\ & \Rightarrow x^2+(2 x+3)^2+6 x-4(2 x+3)+4=0 \\ & \Rightarrow 5 x^2+10 x+1=0 \end{aligned}\) Sum of roots \(x_1+x_2=-\frac{10}{5}=-2\) \(\therefore\) Mid point…
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