Question

(a) use the discriminant to classify the graph,  (b)  use  the  Quadratic  Formula  to  solve  for y, and (c) use a graphing utility to graph the equation.

12x^2 - 6xy + 7y^2 - 45 = 0

Answer 1

Step 1:

(a)

The conic equation is .

Compare it to general form of conic equation  .

.

And have same signs and unequal, So the equation is ellipse.

Step 2:

(b) The conic equation is

Write the equation in quadratic form

Solutions are

.

Solution :

(a) The conic equation is ellipse.

(b) .

 

Answer 2

Step 1:

The equation .

(c) Choose random values for and solve for .

Graph:

Draw the coordinate plane.

Plot the points found in the table and connect the plotted points.

Solution :

.