Conic Sections Question 486
Question: 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
Options:
A) $ 4-\sqrt{2} $
6
C) $ 4+2\sqrt{2} $
D) $ 4+\sqrt{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
if (a, 0) is the center C and P is (2, -2), then $ \angle COP=45{}^\circ $ . Since the equation of OP is $ x+y=2 $ , we have $ OP=2\sqrt{2}=CP $
Hence, OC=4, The point on the circle with the greatest x coordinate is B. $ \alpha =OB=OC+CB=4+2\sqrt{2} $
BETA
