Question

Let ax + by + c = 0 be a variable straight line, where a, b and c are 1^st, 3^rd and 7^th terms of an increasing A.P. respectively. Then the variable straight line always passes through a fixed point which lies on-

• A. y² = 4x
• B. x² + y² = 5
• C. 3x + 4y = 9
• D. x² + y² = 13

Answer 1

Answer: (D)

x² + y² = 13

Answer 2

Let the common difference of A.P. is d

then b = a + 2d and c = a + 6d, so variable straight line will be

ax + (x + 2d)y + a + 6d = 0

Ž a(a + y + 1) + d(2y + 6) = 0

which always passes through (2, –3).