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f(x , y)=x^2+y^2+2a x+2b y+c=0 represent...

`f(x , y)=x^2+y^2+2a x+2b y+c=0` represents a circle. If `f(x ,0)=0` has equal roots, each being `2,` and `f(0,y)=0` has 2 and 3 as its roots, then the center of the circle is `(2,5/2)` (b) Data are not sufficient `(-2,-5/2)` (d) Data are inconsistent

A

`(2,5//2)`

B

Data are not sufficient

C

`(-2,-5//2)`

D

Data are inconsistent.

Text Solution

Verified by Experts

The correct Answer is:
3
`x^(2)+2ax+c=(x-2)^(2)`
or `-2a=4,c=4`
or `a= -2,c=4`
`y^(2)+2by+c=(y-2)(y-3)`
or `-2b=5,c=6`
or `b=- (5)/(2),c=6`
Clearly, the data are not consistent.
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