Question 750315
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 {{{sqrt(257)/4}}}
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y = 1/x is a hyperbola centered at the Origin
The point is on a circle about the Origin
{{{x^2 + y^2 = 257/16}}} is the circle
Find the intersections.
{{{x^2 + y^2 = 257/16}}}
Sub 1/y for x
{{{y^2 + 1/y^2 = 257/16}}}
{{{16y^4 + 16 = 257y^2}}}
{{{16y^4 - 257y^2 + 16 = 0}}}
{{{(16y^2 - 1)*(y^2 - 16) = 0}}}
{{{y^2 = 16}}}
y = -4 (for Q3)
x = 1/y = -1/4
--> (-1/4,-4)
y = -1/4
x = -4
--> (-4,-1/4)