Question

How many points of intersection are there between the graphs of the hyperbola and ellipse?

Answer 1

The point of intersection is the point where two or more functions meet.

The graphs of the hyperbola and ellipse have 0 point of intersection

The given parameters are:

$\mathbf{3x^2 - 4y^2 + 4x - 8y + 4 = 0}$

$\mathbf{3x^2 + y^2 + 4x - 3y + 4 = 0}$

To determine the points of intersection, we simply equate both equations.

So, we have:

$\mathbf{3x^2 + y^2 + 4x - 3y + 4 = 3x^2 - 4y^2 + 4x - 8y + 4 }$

Cancel out the common terms

$\mathbf{y^2 - 3y = - 4y^2 - 8y }$

Collect like terms

$\mathbf{y^2 +4y^2= 3y - 8y }$

$\mathbf{5y^2= - 5y }$

Divide through by 5

$\mathbf{y^2= - y}$

Divide through by y

$\mathbf{y= -1}$

The system of equation does not give room to calculate the x-coordinate at the x-axis.

Hence, the graphs of the hyperbola and ellipse have 0 point of intersection

Read more about points of intersection at:

brainly.com/question/13373561