What is the point of intersection of x^2 + 4y^2 = 16 and y^2 - x^2 = 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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At the point of intersection of the curves defined by x^2 + 4y^2 = 16 and y^2 - x^2 = 0 the x and y coordinates satisfy both the equations.

y^2 - x^2 = 0

=> x^2 = y^2

Substitute in x^2 + 4y^2 = 16

=> 5x^2 = 16

=> `x = +- 4/sqrt 5`

The points of intersection of the given curves are `(4/sqrt 5, 4/sqrt 5)` ,`(4/sqrt 5,-4/sqrt 5)` ,`(-4/sqrt 5,4/sqrt 5)` and `(-4/sqrt 5,-4/sqrt 5)`

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