Question

The range of g so that we have always a chord of contact of tangents drawn from a real point `(alpha, alpha)` to the circle `x^(2)+y^(2)+2gx+4y+2=0`, is
A. (-3, 0)
B. (-4, 1)
C. (-4, 0)
D. none of these

Answer 1

Correct Answer - C
For a real chord of contact of tangents drawn from `(alpha, alpha)` to the circle `x^(2)+y^(2)=2gx+4y+2=0`, the point `(alpha, alpha)` must lie outside the circle.
`:. alpha^(2)+alpha^(2)+2g alpha + 4 alpha + 2 gt 0`
`rArr alpha^(2)+g alpha + (2 alpha + 1) gt 0`
`rArr alpha^(2)+(g+2)alpha+1gt0`
Since `alpha` assumes real values . Therefore,
`(g+2)^(2)-4 gt = 0`
`rArr g^(2)+4h lt 0 rArr -4 lt g lt 0 rArr g in (-4, 0)`.