First slide

Equation of line in Straight lines

Question

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

Moderate

A

x²+ y² = 4
B

x²+ y² = 13
C

y² = 2x
D

2x + 3y = 9

Solution

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

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