Question

Find  any  points  of  intersection  of  the graphs algebraically and then verify using a graphing utility.

Answer 1

Step 1:

Solve the equations algebraically.

From equation (1):

From equation (2):

Equate the left hand side of equations (3) and (4).

Apply zero product property.

and

and .

Step 2:

Substitute the values in equation (1).

For

For

Intersection points are .

Comments

Contd..

Step 3:

Compare it to general conic form

Discriminant

.

So the equation is hyperbola.

Step 4:

Compare it to general conic form

.

And have same signs and equal, So the equation is circle.

Graph:

Graph the conic equations.

Observe the graph:

Intersection points are and  .