The limiting points of the system of circles represented by the equation `2(x^(2)+y^(2))+lambda x+(9)/(2)=0`, are

Options

A. `(pm(3)/(2), 0)`
B. `(0, 0), ((9)/(2), 0)`
C. `(pm (9)/(2), 0)`
D. `(pm 3, 0)`

Answer

A

Explanation

We have,
`2(x^(2)+y^(2))+lambda x + (9)/(2)=0 rArr x^(2)+y^(2)+(lambda)/(2) x + (9)/(4)=0`
The coordinates of the centre of this circle are `(-lambda//4, 0)`
and, Radius`=sqrt((lambda^(2))/(16)-(9)/(4))=(1)/(4)sqrt(lambda^(2)-36)`
Since limiting points are centres of point circles.
`:.` Radius `= 0 rArr lambda = pm 6`
Hence, limiting points are `(pm (3)/(2), 0)`.