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Ok so this can be done by using pythagorean theorem.
You are given the x value and you also know that the equation of the circle can be written as x^2 + y^2 = r^2. Since this is a unit circle the equation that you are going to get is
x^2 + y^2 = 1. This equation describes your circle. Now put in the x value that you hvae...
(7/25)^2 + y^2 = 1 and now rearrange the equation to solve for y.
y^2 = 1 - (7/25)^2
y = SQRT ( 1 - (7/25)^2 )
So if you square root it you will get a positive and a negative answer. Now, since it is specified that the answer must lie in the second quadrant, then you know it has to be in the quadrant that has -x and a positive y. Hence, you select a positive answer from your square root.
IF it asked to find it in the 3rd quadrant you know that the third quadrant is when all values of x AND y are negative. So in that case you would take the negative value of the square root.