Question

The set of values of a for which the point `(2a, a + 1)` is an interior point of the larger segment of the circle `x^2 + y^2 - 2x - 2y - 8 = 0` made by the chord `x - y +1 = 0`, is
A. (-1,9/5)
B. (0, 9/5)
C. `(0, oo)`
D. none of these

Answer 1

Correct Answer - B
The point (2a, a+1) will be an interior point of the larger segment of the circle `x^(2)+y^(2)-2x-2y-8=0`,
if (i) the point (2a, a+1) and the centre (1, 1) are on the same side of the chord `x-y+1=0`.
`:. (2a)^(2)+(a+1)^(2)-2(2a)-2(a+1)-8 lt 0`
and,
`(2a-a-1+1)(1-1+1)lt 0`
`rArr 5a^(2)-4a-9 lt 0` and `agt0`
`rArr (5a-9) (a+1) lt 0` and `a gt 0`
`-1 lt a lt (9)/(5)` and `a gt 0 rArr a in (0, 9//5)`