Download Every conic section may be written in the form:

7-6 General Conic Form
Expand the binomial.
Factor the trinomial.
1. (x + 3)2 =
2. x2 – 12x + 36
**Remember**
x2 + bx + c
In terms of b, c = _____
What term is needed to complete the square?
a2 + 8a + c
c = ______
Complete the Square.
3. x2 + 6x + 8 = 0
____ + ____ = ____
____ + ____ + ____ = ____ + ____
( ____ + ____ )2 = ____
HINTS:
1. Move the constant
to the other side.
2. Divide everything by
the coefficient of x2
(if there is one)
3. Add the new
number to BOTH
sides.
4. Factor.
4. 4x2 + 8x - 16 = 0
____ + ____ = ____
____ + ____ = ____
____ + ____ + ____ = ____ + ____
( ____ + ____ )2 = ____
Every conic section may be written in the form
Ax2 + Bxy + Cy² + Dx + Ey + F = 0
Assume B = 0
Look at values of A and C (the two quadratic coefficients)
Conic Section
Relationship of A and C
Parabola
A = 0 or C = 0
only one squared term
Circle
A=C
Ellipse
A and C
same sign
different numbers.
Hyperbola
A and C
different signs.
Standard Form
y k  
1
x  h2 or x  h   1 y  k 2
4c
4c
(x - h)2 + (y - k)2 = r2
( x  h)
a
2
2

(y  k)
b
2
2
2
2
( x  h)
(y  k)
 1 or

1
2
2
b
a
2
2
( x  h) 2 ( y  k ) 2
or ( y  k )  ( x  h)  1


1
a2
b2
a2
b2
Convert each equation into standard form by completing the square.
5. x2 + y2 + 10x – 4y + 20 = 0
11. 11x2 – 4y2 – 22x – 16y – 49 = 0
6. 3x2 + 3y2 - 6x + 24y + 24 = 0
(Divide everything by 3 first!)
12. 4y2 – x2 + 2x + 24y + 19 = 0
7. x² + 8y + 4x - 4 = 0
13. 25x2 – 4y2 + 16y – 116 = 0
8. y² - 8x - 6y - 7 = 0
9. 9x2 + 25y2 + 36x – 150y + 36 = 0
10. 5x² + 4y² – 32y – 16 = 0