(e) show that the point of intersection of the circle x^2 + y^2 - 6x + 2y - 17 =

Question

(e) show that the point of intersection of the circle x^2 + y^2 - 6x + 2y - 17 =0 and the line x-y+2=0 are the end points of a diameter of the circle x^2 + y^2 - 4y - 5 =0

Explanation / Answer

you solve the first two equations and get two points. then you plugthoes two points into the third equation and see that they aretrue. you also will need thoes two points to make a line and usethat line to see if the center of the circle made by the thirdequation is on that line. when you use the first two equations you get these two points {{x -> -(3/Sqrt[2]), y -> 1/2 (4 - 3 Sqrt[2])} {x -> 3/Sqrt[2], y -> 1/2 (4 + 3 Sqrt[2])}} chang the circle eqution to the circle equation form x^2 + y^2 - 4y - 5 =0 (x+0)^2+(y-2)^2=9 center is (0,2) we are not supposed to give the answers. but i know you can make aline from the two points. put it in the circle equation. getthe intercetion points. and see if the center of the circle is onthe line.

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