Question

In the system shown below, what are the coordinates of the solution that lies in

quadrant II?
Write your answer in the form (a, b) without using spaces.
x² + y²=5
y=1/4x^2

Answer 1

The solution in second quadrant is (-2,1).

Explanation:

We have two equations and we have to solve them to get two unknowns.

The equations are

x² + y² = 5 ......... (1) and

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

⇒ x² = 4y ....... (2)

Now, solving (1) and (2) we get

y² + 4y - 5 = 0

⇒ y² + 5x - x - 5 = 0

⇒ (y + 5)(y - 1) = 0

Therefore, y = - 5 or y = 1

Now, for y = - 5, from equation (2), we get x² = 4 (- 5) = - 20 which is not possible.

Hence, y = 1 and then x² = 4, ⇒ x = ± 2.

So the solutions are (2,1) or (-2,1).

Therefore, the solution in the second quadrant is (-2,1). (Answer)