# CLASSIFYING CONIC SECTIONS BY ITS GENERAL EQUATION WORKSHEET

Put each of the following equations in standard form and classify the conic.

Problem 1 :

9y2 – x2 + 2x + 54y + 62 = 0

Solution

Problem 2 :

4x2 + y2 - 8x + 4y - 16 = 0

Solution

Problem 3 :

x2 + y2 + 6x - 4y + 12 = 0

Solution

Problem 4 :

x2 - 2y + 16x + 28 = 0

Solution

## Answer Key

1)

(x - 1)2/144 - (y + 3)2 / 16 = 1

It is in the form of (x - h)2/a2 - (y - k)2 / b2 = 1

It is a hyperbola.

2)

(x - 1)2/4 + (y + 2)2/16 = 1

It is in the form of (x - h)2/a2 + (y - k)2 / b2 = 1

It is a ellipse

3)

(x + 3)2 + (y - 2) = 1

It is in the form of (x - h)2 + (y - k)= r2

It is a circle.

4)

y = (1/2) (x + 4)2  + 6

It is in the form, y = 4a (x - h)2 + k

So, it is parabola.

Classify each conic section and write its equation in standard form.

Problem 1 :

25x2 + 9y2 - 36y - 189 = 0

Solution

Problem 2 :

-2x2 + 20x + y - 44 = 0

Solution

Problem 3 :

-y2 + 2x + 2y + 3 = 0

Solution

Problem 4 :

16x2 + 9y2 - 16x + 18y - 131 = 0

Solution

Problem 5 :

x2 + y2 - 8x + 8y + 31 = 0

Solution

Problem 6 :

2x2 + 2y2 - 14x - 2y + 7 = 0

Solution

1) Ellipse

2)  Parabola

3)  Parabola

4) Ellipse

5) Circle

6)  Circle

## Recent Articles

1. ### Finding Range of Values Inequality Problems

May 21, 24 08:51 PM

Finding Range of Values Inequality Problems

Read More

2. ### Solving Two Step Inequality Word Problems

May 21, 24 08:51 AM

Solving Two Step Inequality Word Problems

Read More

3. ### Exponential Function Context and Data Modeling

May 20, 24 10:45 PM

Exponential Function Context and Data Modeling

Read More