SOLUTION: Find all points satisfying x+y=0 that are 8 units from (-2,3)

Question 1205643: Find all points satisfying x+y=0 that are 8 units from (-2,3)
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!

The points or ordered pairs, (x,-x).

Question asks for all points (x,-x) which are 8 units distance from (-2,3).

, applying the Distance Formula
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Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

Points that are 8 units from (-2,3) are on the circle

Solve x+y = 0 for y to get y = -x

Plug y = -x into to get

Do a bit of algebra to get the following

Now apply the quadratic formula with: a = 2, b = 10, c = -51

or

or

or
Each decimal value is approximate.

Each of those x values is plugged into y = -x to find their corresponding paired y value.

The two answer points are approximately (3.134714, -3.134714) and (-8.134714, 8.134714) which I've marked as points A and B respectively.

Point A is located at roughly (3.134714, -3.134714)
Point B is located at roughly (-8.134714, 8.134714)
Point C is the center of the circle which is (-2,3)
AC = 8 and BC = 8 since any point on the circle is 8 units from point C.
Desmos and GeoGebra are two graphing tools I recommend.

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