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Let A(1, 2), B(3, 4) be two points and C...

Let A(1, 2), B(3, 4) be two points and C(x, y) be a point such that area of `DeltaABC` is 3 sq. units and `(x- 1)(x-3)+ (y-2)(y-4)=0`. Then number of positions of C, in the xy plane is

A

2

B

4

C

8

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
(x,y) lies on the circle with AB as a diameter.
Diameter `AB = 2 sqrt(2)`
`:.` Radius `= sqrt(2)`
Area `(DeltaABC) =3`
`rArr ((1)/(2)) (AB) xx ("alitude") =3`
`rArr` Altitude `=(3)/(sqrt(2)) gt` Radius
Hence, no such C exists.
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