Chapter 8.6, Problem 2E

Solution

To explain : The use of the discriminant of a general second-degree equation to identify the conic equation it represents.

The value of the discriminant of a general second-degree equation helps to identify the conic equation it represents.

Given information :

The discriminant of a general second-degree equation.

Explanation :

A general second-degree equation is $a{x}^2+bx+c=0$ .

The discriminant of a general second-degree equation is $b^2-4ac$ .

When $b^2-4ac<0,b=0\text{ and }a=c$ , then the conic is a circle.

When $b^2-4ac<0$ , and either $b\ne 0\text{ or }a\ne c$ then the conic is an ellipse.

When $b^2-4ac=0$ , then the conic is a parabola.

When $b^2-4ac>0$ , then the conic is a hyperbola.

Therefore value of the discriminant of a general second-degree equation helps to identify the conic equation it represents.