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Question
Choose the correct alternative:
If the lines 2x − 3y = 5 and 3x − 4y = 7 are the diameters of a circle of area 154 sq. units, then find the equation of the circle
Options
x2 + y2 − 2x + 2y = 40
x2 + y2 − 2x + 2y = 40
x2 + y2 − 2x + 2y = 47
x2 + y2 − 2x − 2y = 40
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Solution
x2 + y2 − 2x + 2y = 47
Explanation:
Centre of circle = Point of intersection of diameters.
Solving 2x – 3y = 5 and 3x – 4y = 7, we get x = 1, y = - 1
Centre of the circle C (h, k) = C (1, –1)
Area = 154
∴ πr2 = 154
∴ `22/7 xx "r"^2 = 154`
∴ `"r"^2 = 154 xx 7/22` = 49
∴ r = 7
∴ equation of the circle is
(x - 1)2 + (y + 1)2 = 72
∴ x2 + y2 − 2x + 2y = 47
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