AP EAMCET · Maths · Circle
The lengths of the tangents from the point \((1,2)\) to the circle \(x^2+y^2+x+y-4=0\) and \(3 x^2+3 y^2-x-y-k=0\) are in the ratio \(4: 3\), then the value of \(k\) is
- A \(\frac{9}{4}\)
- B \(\frac{13}{4}\)
- C \(\frac{17}{4}\)
- D \(\frac{21}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{21}{4}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } C_1: x^2+y^2+x+y-4=0 \\ & C_2: 3 x^2+3 y^2-x-y-k=0 \\ & \Rightarrow \quad x^2+y^2-\frac{x}{3}-\frac{y}{3}-\frac{k}{3}=0\end{aligned}\) Length of tangents drawn from external point to the circle is \(\sqrt{S_1}\). Now, according to the question, Let…
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