SOLUTION: Please help me with the following problem: Q/. Point (a,b) lies in the third quadrant on the graph of the equation y = 1/x. Find a and b given that the distance from poin (a,b)

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Question 750315: Please help me with the following problem:
Q/. Point (a,b) lies in the third quadrant on the graph of the equation y = 1/x. Find a and b given that the distance from poin (a,b) to the origin is .
A/. y = 1/x ; b = 1/a ; a = 1/b

I'm stuck at solving for a....I tried to rearrange it as but I don't know if this brings me any closer to the answer..
The textbook answer is a = -1/4, -4. Thanks..
Found 2 solutions by rothauserc, Alan3354:
Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
the problem states
Q/. Point (a,b) lies in the third quadrant on the graph of the equation y = 1/x. Find a and b given that the distance from point (a,b) to the origin is
(sqrt(257)/4)
note that a point in the third quadrant has a negative x and negative y. Also
y = 1/x has components in the first and third quadrants
The point (a,b) lies on the line y = 1/x in the third quadrant, we know
X^2 + (1/x)^2 = 257 / 16
note that 16 is 4^2
so if x = -4 then y = - 1/4
and 16 + (1/16) = (16^2 + 1) / 16 = 257 / 16

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Point (a,b) lies in the third quadrant on the graph of the equation y = 1/x. Find a and b given that the distance from poin (a,b) to the origin is
------------------
y = 1/x is a hyperbola centered at the Origin
The point is on a circle about the Origin
is the circle
Find the intersections.

Sub 1/y for x

y = -4 (for Q3)
x = 1/y = -1/4
--> (-1/4,-4)
y = -1/4
x = -4
--> (-4,-1/4)