AP EAMCET · Maths · Circle
If \(\theta\) is the angle between the tangents drawn from the point \((-1,-1)\) to the circle \(x^2+y^2-4 x-6 y+c=0\) and \(\cos \theta=-\frac{7}{25}\), then the radius of the circle is
- A \(4\)
- B \(1\)
- C \(2\)
- D \(3\)
Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
Center of circle: \( (2,3) \) Distance from center to \((-1,-1)\): \(d = \sqrt{(2-(-1))^2 + (3-(-1))^2} = \sqrt{3^2+4^2} = \sqrt{25} = 5 \) Given \(\cos \theta = -\frac{7}{25}\), and \(\cos \theta = 2\left(\frac{L}{d}\right)^2 - 1 \), where \(L\) is the length of the tangent.…
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