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Step-by-step explanation:
The equation will form a circle because it in the form of
[tex](x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]
First, let set the equation equal.
[tex](x - 7) {}^{2} + (y + 5) {}^{2} = 25[/tex]
Here the center will be (7,-5), and the radius of 5. The boundary line will be dashed
Since this is in the inequalities, we must find the solution set.
Plug in 0,0 for x and y and see if it's true.
[tex](0 - 7) {}^{2} + (0 + 5) {}^{2} > 25[/tex]
[tex]49 + 25 > 25[/tex]
[tex]74 > 25[/tex]
This is a true so we shade the region that includes 0,0
Since 0,0 has a greater distance from the center of the circle, 0,0 is outside of the circle, so our solution set will
be outside of circle.
Here a picture of graph,
