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If `(alpha,beta)` is a point on the circle whose center is on the x-axis and which touches the line `x+y=0` at `(2,-2),` then the greatest value of `alpha` is `4-sqrt(2)` (b) 6 `4+2sqrt(2)` (d) `+sqrt(2)`

A

`4-sqrt(2)`

B

6

C

`4+2sqrt(2)`

D

`4+sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
3
If (a,0) is the center C and P is P is (2,-2) , then `/_ COP =45^(@)`.

Since the equation of OP is `x+y=0`, we have
`OP =2sqrt(2)=CP`
Hence, `OC=4`.
The point on the circle with the greatest x coordinate is B.
`alpha = OP=OC+CB=4+2sqrt(2)`
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