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Equation of a Circle Quiz

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Questions and Answers

Which of the following is the standard form of the equation of a circle with a radius of 7 and a center at (0,0)?

$x^2 + y^2 = \sqrt{7}$
$x^2 + y^2 = 49$ (correct)
$x^2 + y^2 = \sqrt{49}$
$x^2 + y^2 = 7^2$

Which of the following is the standard form of the equation of a circle with a radius of √2 and a center at (0,0)?

$x^2 + y^2 = \sqrt{2}$
$x^2 + y^2 = (\sqrt{2})^2$ (correct)
$x^2 + y^2 = \sqrt{\sqrt{2}}$
$x^2 + y^2 = 2$

Which of the following is the standard form of the equation of a circle with a radius of 9 and a center at (0,0)?

$x^2 + y^2 = \sqrt{81}$
$x^2 + y^2 = 9^2$
$x^2 + y^2 = 81$ (correct)
$x^2 + y^2 = \sqrt{9}$

Which of the following is the standard form of the equation of a circle with a radius of √5 and a center at (8,-4)?

<p>$x^2 + y^2 = (\sqrt{5})^2$ (A)</p> Signup and view all the answers

Which of the following is the standard form of the equation of a circle with a radius of 1 and a center at (3,5)?

<p>$(x-3)^2 + (y-5)^2 = 1^2$ (C)</p> Signup and view all the answers

Flashcards

Standard Form of a Circle's Equation

The standard form of the equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

Equation of a Circle Centered at the Origin

The equation of a circle with a center at the origin (0,0) is x^2 + y^2 = r^2, where r is the radius. This is a simplified version of the standard form.

Circle Equation: Radius 7, Center (0,0)

The equation of a circle with a radius of 7 and a center at (0, 0) is x^2 + y^2 = 49. This is because 7 squared is 49.

Circle Equation: Radius √2, Center (0,0)

The equation of a circle with a radius of √2 and a center at (0, 0) is x^2 + y^2 = (√2)^2. This is because (√2) squared is 2.

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Circle Equation: Radius 1, Center (3,5)

When the center of the circle is not at the origin, the equation of the circle is (x - h)^2 + (y - k)^2 = r^2. For a circle with a radius of 1 and a center at (3, 5), the equation becomes (x - 3)^2 + (y - 5)^2 = 1^2.

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Study Notes

Circle Equations

Standard form of a circle equation with a radius of 7 and a center at (0,0): x² + y² = 49
Standard form of a circle equation with a radius of √2 and a center at (0,0): x² + y² = 2
Standard form of a circle equation with a radius of 9 and a center at (0,0): x² + y² = 81
Standard form of a circle equation with a radius of √5 and a center at (8,-4): (x-8)² + (y+4)² = 5
Standard form of a circle equation with a radius of 1 and a center at (3,5): (x-3)² + (y-5)² = 1

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