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JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
If each of the lines \(5x + 8y = 13\) and \(4x - y = 3\) contains a diameter of the circle
\(x^2 + y^2 - 2\,(a^2 - 7a + 11)\) \(x - 2\, ( a^2 - 6a + 6)\, y + b^3 + 1 = 0\), then
- A \(a = 5\) and \(b \notin \left( { - 1,1} \right)\)
- B \(a = 1\) and \(b \notin \left( { - 1,1} \right)\)
- C \(a = 2\) and \(b \notin \left( { - \infty ,1} \right)\)
- D \(a = 5\) and \(b \in \left( { - \infty ,1} \right)\)
Answer & Solution
Correct Answer
(D) \(a = 5\) and \(b \in \left( { - \infty ,1} \right)\)
Step-by-step Solution
Detailed explanation
Point of intersection of two given lines is \((1,1)\). Since each of the two given lines contains a diameter of the given circle, therefore the point of intersection of the two given lies is the centre of the given circle. Hence centre \(=(1,1)\)…
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