Question

Quadratic equation in two variables related to conic section

Answer 1

Answer:

Examples.

• 4x2  3xy  2y2 + x  y + 6 = 0 is a quadratic equation, as are

x2  y2 = 0 and x2 + y2 = 0 and x2  1 = 0.

• y = x2 is a quadratic equation. It’s equivalent to y  x2 = 0,

and y  x2 is a quadratic polynomial.

• xy = 1 is a quadratic equation. It’s equivalent to the quadratic

equation xy  1 = 0.

• x2+y2 = 1 is a quadratic equation. It’s equivalent to x2+y2+1 = 0.

• x2 + y = x2 + 2 is a not a quadratic equation. It’s a linear equation.

It’s equivalent to y  2 = 0, and y  2 is a linear polynomial.

A conic is a set of solutions of a quadratic equation in two variables. In

contrast to lines–solutions of linear equations in two variables–it takes a fair

amount of work to list all of the possible geometric shapes that can possibly

arise as conics. In what remains of this chapter, we’ll take a tour of some

conics that we already know. After we cover trigonometry in this course,

we’ll return to conics and explain all of the possible shapes of conics.