SOLUTION: Point P (-4,a) and point (4,b) are both 5 units away from the origin. What's the maximum possible length for segment PQ? This is a multiple choice problem. a)7 b)8 c)9 d)10

Algebra ->  Length-and-distance -> SOLUTION: Point P (-4,a) and point (4,b) are both 5 units away from the origin. What's the maximum possible length for segment PQ? This is a multiple choice problem. a)7 b)8 c)9 d)10       Log On


   

Question 886102: Point P (-4,a) and point (4,b) are both 5 units away from the origin. What's the maximum possible length for segment PQ? This is a multiple choice problem.
a)7
b)8
c)9
d)10
e)11
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
The two given points are on the circle x%5E2%2By%5E2=5%5E2. You can find a or b and use some sense of knowing where the points are on the circle to decide where the maximum length of PQ would show. a and b are the two y-coordinates.

y%5E2=25-x%5E2
highlight_green%28y=0%2B-+sqrt%2825-x%5E2%29%29, TWO DIFFERENT VALUES.
You should be able to finish this.

Note that the four points will form a rectangle, and what YOU want is the coordinates of either or both DIAGONALs. (Use the Distance Formula to find the diagonal length.)