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Understanding circles and tangents in the coordinate plane

Algebra • Graphs

Key concepts

What you'll likely be quizzed about

  • A circle is defined as the set of all points in a plane equidistant from a central point known as the center.
  • The fixed distance is the radius.
  • The standard equation of a circle with center (h, k) and radius r is (x - h)² + (y - k)² = r².
  • This equation helps identify any circle within the coordinate system.

Flashcards

Test your knowledge with interactive flashcards

How do you find the equation of a tangent line?

Click to reveal answer

To find the equation of a tangent line, first determine the slope of the radius to the tangential point, and then use its negative reciprocal.

Key notes

Important points to keep in mind

The equation of a circle varies based on the center and radius.

Tangent lines are always perpendicular to the radius at the point of contact.

Recognizing the properties of circles is vital for solving related problems.

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