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Let ax + by + c = 0 be a variable straight line, where a, b and c are first, third and seventh terms of an increasing
A.P. Then, the variable straight line always passes through a fixed point which lies on

a
x2 + y2 = 4
b
x2 + y2 = 13
c
y2 = 2x
d
2x + 3y = 9

detailed solution

Correct option is B

Let d be the common difference of A.P., thenb = a + 2d and c = a + 6d. Clearly, (b – a) × 3 = c – a⇒ 2a – 3b + c = 0Thus, the straight line ax + by + c = 0 passes throughthe point (2, –3) which also satisfies x2 + y2 = 13.

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