Question

The ellipse 4x^2 + 8y^2 = 64 and the circle x^2 + y^2=9 intersect at points where the y coordinate is ____ ? The ellipse 4x^2 + 8y^2 = 64 and the circle x^2 + y^2=9 intersect at points where the y coordinate is ____ ? @Mathematics

Answer 1

when these intersect, their x and y coordinates are the same. since you have been asked to find the y coordinate, you need to use one of the equations to eliminate x, i.e:\[4x^2+8y^2=64\]re-arrange this to get:\[x^2=16-2y^2\]put this into the second equation:\[x^2+y^2=9\]to get:\[16-2y^2+y^2=9\]and solve. hopefully you can do the rest.

Answer 2

\[\left\{y=\sqrt{7}, y=-\sqrt{7}\right\} \]