Equation of a Circle (Edexcel A-Level Mathematics): Flashcards

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Equation of a Circle
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What is the standard equation of a circle at origin?

x2+y2=r2x^2 + y^2 = r^2 defines a circle at the origin.

How to translate a circle's center?

Use (x+a)2+(y+b)2=r2(x + a)^2 + (y + b)^2 = r^2 for translation.

What is the center of the circle from (x+a)2+(y+b)2(x + a)^2 + (y + b)^2?

The center is (−a,−b)(-a, -b) from the circle equation.

How to find the center and radius from x2+3xx^2 + 3x?

Complete the square to find center and radius.

What is the center of (x+3)2+(y−2)2(x + 3)^2 + (y - 2)^2?

Center is (−3,2)(-3, 2) from completed square form.

What is the radius of the circle x2+y2=9x^2 + y^2 = 9?

Radius is 3, since r2=9r^2 = 9.

How do you find the radius with points?

Use r=(x2−x1)2+(y2−y1)2r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.

What is the equation for a circle centered at (2,4)(2, 4) with r=7r=7?

Equation is (x−2)2+(y−4)2=49(x - 2)^2 + (y - 4)^2 = 49.

What is the center of the circle x2+y2=4x^2 + y^2 = 4?

Center is (0,0)(0, 0) with radius 22.

How to find intersection points with a line and circle?

Substitute line into circle equation and solve for xx.

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Equation of a Straight Line

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Equation of a Straight Line

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Equation of a Straight Line

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Equation of a Straight Line

Circles

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