Equation of a circle (AQA GCSE Further Maths): Flashcards

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Equation of a circle
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Equation of circle centered at origin with radius rr

x2+y2=r2x^2 + y^2 = r^2

Equation of circle centered at (a,b)(a,b) with radius rr

(x−a)2+(y−b)2=r2(x-a)^2 + (y-b)^2 = r^2

Two key pieces of info needed for circle equation

Center location and radius

Expanded form of circle equation (general)

x2+y2−2ax−2by+c=0x^2 + y^2 - 2ax - 2by + c = 0

Coefficients of x2x^2 and y2y^2 in expanded circle equation

Both equal to 1

Feature of expanded circle equation involving xyxy

No xyxy term present

Method to find center/radius from expanded form

Completing the square

Angle in a semicircle (Thales' Theorem)

90°

Angle between tangent and radius at point of contact

90° (perpendicular)

Perpendicular from center to chord does what?

Bisects the chord (passes through midpoint)

Two tangents from external point have what property?

Equal length

If radius gradient is mm, tangent gradient is

- rac{1}{m} (negative reciprocal)

Distance formula between (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2)

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

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Coordinate geometry

Geometry I

Geometry II

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Coordinate geometry

Geometry I

Geometry II

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Coordinate geometry

Geometry I

Geometry II

Explore AQA GCSE Further Maths Exam Questions by Topics

Coordinate geometry

Geometry I

Geometry II

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