Using the equation of a circle, it is found that the value of y is -4.
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The equation of a circle of radius r and center [tex](x_0,y_0)[/tex] is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
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The points (0,5) and (0,-5) are the endpoints of the diameter of a circle.
The center is the midpoint of them, thus:
[tex]x_0 = \frac{0 + 0}{2} = 0[/tex]
[tex]y_0 = \frac{5 - 5}{2} = 0[/tex]
The diameter(twice the radius) is the distance between these two points, so:
[tex]2r = \sqrt{(0 - 0)^2 + (5 - (-5))^2}[/tex]
[tex]2r = \sqrt{100}[/tex]
[tex]2r = 10[/tex]
[tex]r = \frac{10}{2}[/tex]
[tex]r = 5[/tex]
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Thus, the equation of the circle is:
[tex]x^2 + y^2 = 5^2[/tex]
[tex]x^2 + y^2 = 25[/tex]
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The point (3,y) is on the circle, in quadrant 4. This means that:
Then:
[tex]3^2 + y^2 = 25[/tex]
[tex]y^2 = 16[/tex]
[tex]y = \pm \sqrt{16}[/tex]
[tex]y = -4[/tex]
The value of y is -4.
A similar problem is given at https://brainly.com/question/23719612
