CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 9. Conics

sides of thex^2 square.

Notice what is missing to make this shape a perfect square? A little corner square of 9 is missing which is why the
9 should be added to make the perfect square of(x+ 3 )(x+ 3 ).
Example B
What type of conic is each of the following relations?

a. 5y^2 − 2 x^2 =− 25

b.x=−^12 y^2 − 3

c. 4x^2 + 6 y^2 = 36

d.x^2 −^14 y= 1

e.−x 82 +y 42 = 1

f. −x^2 + 99 y^2 = 12

Solution:

a. Hyperbola because thex^2 andy^2 coefficients are different signs.

b. Parabola (sideways) because thex^2 term is missing.

c. Ellipse because thex^2 andy^2 coefficients are different values but the same sign.

d. Parabola (upright) because they^2 term is missing.

e. Hyperbola because thex^2 andy^2 coefficients are different signs.

f. Hyperbola because thex^2 andy^2 coefficients are different signs.

Example C
Complete the square for both thexandyterms in the following equation.
x^2 + 6 x+ 2 y^2 + 16 y= 0