X2 + y2 = 25 y2- x2 = 7 the solutions?

2 Answers

Oddman Profile
Oddman answered
Add the two equations together to find y, then use that to find x.
  (x^2 + y^2) + (y^2 - x^2) = (25) + (7)
  2y^2 = 32    (collect terms)
  y^2 = 16    (divide by 2)
  y = +/- sqrt(16) = +/- 4
  x^2 + 16 = 25    (substitute for y^2 in the first equation)
  x^2 = 9    (subtract 16)
  x = +/- sqrt(9) = +/- 3

The points of intersection of the circle and hyperbola are
  (3, 4), (3, -4), (-3, -4), (-3, 4)
John McCann Profile
John McCann answered
Is this a system? Or, just parts of a circle?

For instance,

X^2 + Y^2 = 25

Y^2 = 25 - X^2

Y = (+/-)  sqrt(25 - X^2)

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Anonymous