Understanding the Standard Form of a Circle
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Questions and Answers

What is the standard form of a circle?

  • E = mc^2
  • (x - h)^2 + (y - k)^2 = r^2 (correct)
  • a^2 + b^2 = c^2
  • y = mx + c

What does the equation (x - 3)^2 + (y + 4)^2 = 16 represent?

  • An ellipse
  • A hyperbola
  • A parabola
  • A circle (correct)

In the standard form of a circle, what does 'r' represent?

  • Radius (correct)
  • Intercept
  • Center
  • Slope

If a circle has its center at (1, -2) and radius 5, what is its standard form equation?

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

What happens to the equation of a circle if its center is at (0,0)?

<p>The 'h' and 'k' terms become zero (B)</p> Signup and view all the answers

What is the general formula for the distance between two points (x1, y1) and (x2, y2)?

<p>$ ext{sqrt}((x1 - x2)^2 + (y1 - y2)^2)$ (C)</p> Signup and view all the answers

What does the discriminant of the equation of a circle determine?

<p>The shape of the circle (D)</p> Signup and view all the answers

If the radius of a circle is doubled, what happens to its area?

<p>It becomes four times (B)</p> Signup and view all the answers

What is the relationship between the radius and diameter of a circle?

<p>$d = 2r$ (B)</p> Signup and view all the answers

If two circles have the same radius, what can be said about their areas?

<p>They are equal (D)</p> Signup and view all the answers

Study Notes

TheEquation of a circle

The standard form of the circle

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This quiz covers the standard form of a circle, including its equation and properties. Test your knowledge about the characteristics and concepts related to the standard form of a circle.

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