The type of conic sections for the nondegenerate equations given below.
a)
b)
c)
The type of conic sections for the nondegenerate equations given below.
a)
b)
c)
a) Consider the equation
This equation can be written as:
It is known that the equation is in the form of
Here, the coefficient of
Therefore, the equation is of a hyperbola. Hence, the conic section of the given equation is a hyperbola.
b) Consider the equation
This equation caan be written as:
Solve for
This shows that
c) Consider the equation
his equation can written as:
Therefore, the equation is of an ellipse. Hence, the conic section of the given equation is an ellipse.
To determine: The conic section and to find the vertices and foci: