Question

Statement-1: If limiting points of a family of co-axial system of circles are (1, 1) and (3, 3), then `2x^(2)+2y^(2)-3x-3y=0` is a member of this family passing through the origin.
Statement-2: Limiting points of a family of coaxial circles are the centres of the circles with zero radius.
A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Answer 1

Correct Answer - A
Statement-2, is true as it is the definition of limiting points.
The members of the family of coaxial circles having (1, 1) and (3, 3) as limiting points are:
`(x-1)^(2)+(y-1)^(2)=0 and (x-3)^(2)+(y-3)^(2)=0`
S0, the equation of the family of co-axial circles is
`{(x-1)^(2)+(y-1)^(2)}+lambda{(x-3)^(2)+(y-3)^(2)}=0 " " ...(i)`
If it passes through the origin, then `lambda=-(1)/(9)`.
Putting `lambda=-(1)/(9)` in (i), we obtain `2x^(2)+2y^(2)-3x-3y=0` as a member of the family of coaxial circles that passes through the origin. So, statement-1 is also true.