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Consider three circles C(1), C(2) and C(...

Consider three circles `C_(1), C_(2)` and `C_(3)` as given below:
`C_(1) : x^(2)+y^(2)+2x-2y+p=0`
`C_(2) : x^(2)+y^(2)-2x+2y-p=0`
`C_(3) : x^(2)+y^(2)=p^(2)`
Statement-1: If the circle `C_(3)` intersects `C_(1)` orthogonally , then `C_(2)` does not represent a circle.
Statement-2: If the circle `C_(3)` intersects `C_(2)` orthogonally, then `C_(2)` and `C_(3)` have equal radii.

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.

Text Solution

Verified by Experts

The correct Answer is:
D
If circles `C_(3) and C_(1)` intersect orthogonally, then
`0+0=p-p^(2)rArrp=1 " " [:'p!=0]`
For `p=1, C_(2):(x-1)^(2)+(y+1)^(2)=3`, which represents a circle.
So, statement-1 is false.
If circles `C_(3)and C_(2)` intersect orthogonally, then
`0+0=-p-p^(2) rArr p=-1 " " [:' p!=0]`
For `p=-1, C_(2):(x-1)^(2)+(y+1)^(2)=1 and C_(3):x^(2)+y^(2)=1`.
Clearly, `C_(2)and C_(3)` have equal radii. So, statement-2 is true.
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