The equation of a circle whose center lies on x + 2y = 0 and touching the lines 3x - 4y + 8 = 0 and 3x - 4y - 28 = 0 is

MHT CET 2026 Mathematics question

The equation of a circle whose center lies on and touching the lines and is

(A)
(B)
(C)
(D)Correct

Answer: (D)

Solution

The two tangents are parallel, so the diameter equals the distance between them: , hence and . The centre lies midway between the lines, i.e. on (average of and is ), and also on

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Question ID VK-101507