How many points of intersection are there between the graphs of the hyperbola and ellipse?
Equate them.....because when they are equal is when they have an intersection/common point
3x^2+4y^2+3x−2y+3=3x^2−2y^2+3x−y+3 delete 3x^2 and 3x from both sides
4y^2 -2y+3 = -2y^2-y+3 gather like terms on one side
6y^2 -y = 0
y(6y-1) = 0 y = 0 or 1/6 now that you have values for 'y' sub back into one of the original equations to fing the corresponding 'x' values.
SO there is 2 points of intersection.
This is an interesting problem because the first equation: 3x2 + 4y2 + 3x - 2y + 3 = 0 does not have a real-valued graph.
If you attempt to place this graphing form: 3x2 + 3x + 4y2 - 2y + 3 = 0
3(x2 + x) + 4(y2 - ½y) = -3
Completing the squares: 3(x2 + x + ¼) + 4(y2 - ½y + 1/16) = -3 + 3/4 + 1/4
3(x + ½)2 + 4(y - ¼)2 = -2
This is not a real-valued function.
So, the points of intersection do not exist in a real-valued plane.