JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let the centre of the circle \(x^2 + y^2 + 2gx + 2fy + 25 = 0\) be in the first quadrant and lie on the line \(2x - y = 4\). Let the area of an equilateral triangle inscribed in the circle be \(27\sqrt{3}\). Then the square of the length of the chord of the circle on the line \(x = 1\) is _______.
- A 20
- B 40
- C 60
- D 80
Answer & Solution
Correct Answer
(D) 80
Step-by-step Solution
Detailed explanation
The equation of the circle is \(x^2 + y^2 + 2gx + 2fy + 25 = 0\). The centre of the circle is \((-g, -f)\). Since it lies in the first quadrant, \(-g > 0\) and \(-f > 0\), which implies \(g < 0\) and \(f < 0\). The centre lies on the line \(2x - y = 4\), so:…
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