Question

Describe the graph that is produced by the equation (x-7)^2+(y+5)^2>25

Answer 1

Explanation:

The equation will form a circle because it in the form of

`(x - h) {}^(2) + (y - k) {}^(2) = {r}^(2)`

First, let set the equation equal.

`(x - 7) {}^(2) + (y + 5) {}^(2) = 25`

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.

`(0 - 7) {}^(2) + (0 + 5) {}^(2) > 25`

`49 + 25 > 25`

`74 > 25`

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,