Practice Standard Equation Of An Ellipse (6.4.1) - Conic Sections - ICSE 11 Maths

Practice: Standard Equation of an Ellipse

Lesson 6.4.1Conic Sections

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8 questions

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6 sample questions

Question 1.
Write the standard equation of an ellipse with semi-major axis 4 and semi-minor axis 2.
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Use the formula \$ \\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 \$.
Question 2.
What is the length of the semi-major axis of an ellipse if $a = 5$ ?
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Refer to the variable \$ a \$ in the equation.
3Question 3.
What is the standard form of an ellipse centered at the origin?
- \$ \\frac{y^2}{a^2} + \\frac{x^2}{b^2} = 1 \$
- \$ \\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1 \$
- \$ x^2 + y^2 = r^2 \$
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Focus on the role of \$ a \$ and \$ b \$.
4Question 4.
True or False: The foci of an ellipse are always located on the minor axis.
- True
- False
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Consider how the axes are defined in an ellipse.
Question 5.
Design an elliptical garden using a semi-major axis of 8 and a semi-minor axis of 3. Write down the equation and describe the distance between the foci.
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Remember to apply the equation for focal distance.
Question 6.
An astronomer wants to track an elliptical orbit with a focus at the sun. If the semi-major axis is 10 million kilometers, and the semi-minor axis is 8 million kilometers, find the foci and write the standard equation.
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Do not forget the equations for \$ c \$ and the standard form.

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