# Worksheet: Identifying Conic Sections

In this worksheet, we will practice converting the general form of conic section equations into any of the standard forms.

Q1:

Consider the conic given by the equation .

Write the equation in standard form.

• A
• B
• C
• D
• E

Hence, describe the conic.

• AAn ellipse with center
• BA circle with center
• CA hyperbola with center
• DA hyperbola with center
• EAn ellipse with center

Q2:

Which type of conic is described by the equation ?

• AA parabola
• BA circle
• CAn ellipse
• DA hyperbola

Q3:

By calculating the discriminant, identify the type of conic that is described by the equation .

• AA parabola
• BAn ellipse
• CA circle
• DA hyperbola

Q4:

The general equation of a conic has the form .

Consider the equation .

Calculate the value of the discriminant .

Hence, identify the conic described by the equation.

• AParabola
• BHyperbola
• CEllipse
• DCircle

Q5:

The general equation of a conic has the form .

Which of the following conditions would allow us to conclude that it is an ellipse?

• A and either or
• B , , and
• C
• D