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MAT - Conics Part 1
供稿人: Plesek
(原作者: Lehnert)

Write the equation of the conic in standard form

and then identify the conic.

 

x2 + 4x +y2 - 2y = 11

x2 + 4x +
+ y2 - 2y +
= 11 +
+

Write the equation of the conic in standard form

and then identify the conic.

 

x2 + 4x +y2 - 2y = 11

x2 + 4x + 4
(x +

)2 + (y  -

+ y2 - 2y + 1
= 11 + 4 + 1
)2 =

Write the equation of the conic in standard form

and then identify the conic.

 

x2 + 4x +y2 - 2y = 11

x2 + 4x + 4
(x + 2

)2 + (y  - 1

+ y2 - 2y + 1

Hyperbola

Circle

Ellipse

Parabola

)2 = 16
= 11 + 4 + 1
What is the center and radius of the circle?
(x + 2

(2, -1) and r = 4

 (2, -1) and r = 16

(-2, 1) and r = 16

(-2, 1) and r = 4

)2 + (y  - 1

)2 = 16

9x2 - 4y2 - 18x - 16y = 43

9(x2 -
x +
)
- 4(y2 + 4y +
)=

9x2 - 4y2 - 18x - 16y = 43

9(x2 - 2x + 1) - 4(y2 +4y + 4) = 36
9(x -
)2 - 4(y +
)2 = 36

9x2 - 4y2 - 18x - 16y = 43

9(x2 - 2x + 1) - 4(y2 +4y + 4) = 36
9(x - 1)2 - 4(y + 2)2 = 36

(x - 1)2 - (y + 2)2

=
Identify the conic.

(x - 1)2 - (y + 2)2

4

Hyperbola

Circle

Ellipse

Parabola

9
=
1

4y2 - 3x + 7x2 - 7y = 18

Tell whether the equation is a circle, ellipse,

parabola or hyperbola.

Circle

Ellipse

 Parabola

Hyperbola

Tell whether the equation is a circle, ellipse,

parabola or hyperbola.

y2 + 9y = 7x + 3x2 + 52

Circle

Ellipse

 Parabola

Hyperbola

Tell whether the equation is a circle, ellipse,

parabola or hyperbola.

2x2 + 4x +2y2 + 6y = 66

Circle

Ellipse

 Parabola

Hyperbola

Tell whether the equation is a circle, ellipse,

parabola or hyperbola.

5y2 + 6x - 10y = 50

Circle

Ellipse

 Parabola

Hyperbola

Tell whether the equation is a circle, ellipse,

parabola or hyperbola.

x2 + 25y2 - 6x - 100y +84 = 0

Circle

Ellipse

 Parabola

Hyperbola

Tell whether the equation is a circle, ellipse,

parabola or hyperbola.

6xy = 96

Circle

Ellipse

 Parabola

Hyperbola

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