SOLUTION: In the system shown below, what are the coordinates of the solution that lies in quadrant II? Write our answer in the form (a,b) without using spaces. x^2+y^2=5 y=1/4x^2 can I g

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: In the system shown below, what are the coordinates of the solution that lies in quadrant II? Write our answer in the form (a,b) without using spaces. x^2+y^2=5 y=1/4x^2 can I g      Log On


   

Question 1100656: In the system shown below, what are the coordinates of the solution that lies in quadrant II? Write our answer in the form (a,b) without using spaces. x^2+y^2=5 y=1/4x^2
can I get a hand with this thank you.
Answer by ikleyn(52830) About Me  (Show Source):
You can put this solution on YOUR website!
.
x^2 + y^2 = 5        (1)

y = (1/4)*x^2        (2)


From eq(2) express x^2 = 4y.  Next, replace x^2 in the eq(1) by 4y, based on it.


You will get a single equation for the unknown y:

4y^2 + y^2 = 5  ====>  5y^2 = 5  ====>  y^2 = 1  ====>  y = +/- 1/


Since  y = (1/4)*x*2, y can not be negative; hence the solution y = -1 does not work,  and we actually have only ONE solution y = 1


If y = 1 then  x^2 + 1^2 = 5  ====>  x^2 = 5-1 = 4  ====>  x = +/- 2.


Thus you have TWO solutions for the original system:  (2,1) and (-2,1).


Of them, only the solution (-2,1) lies in QII.

Solved.