Finding the Centre & Radius (AQA A-Level Mathematics): Flashcards

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Finding the Centre & Radius
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Standard form of circle equation

(x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2

Centre in (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2

(h,k)(h, k)

Radius in (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2

rr

General form of circle equation

x2+y2+Dx+Ey+F=0x^2 + y^2 + Dx + Ey + F = 0

How to find centre/radius from general form?

Complete the square for xx and yy

Completing square: value to add to x2+bxx^2 + bx

( rac{b}{2})^2

Centre of (x−3)2+(y+2)2=16(x - 3)^2 + (y + 2)^2 = 16

(3,−2)(3, -2)

Radius of (x−3)2+(y+2)2=16(x - 3)^2 + (y + 2)^2 = 16

44

Centre of x2+y2+4x−6y−12=0x^2 + y^2 + 4x - 6y - 12 = 0

(−2,3)(-2, 3)

Radius of x2+y2+4x−6y−12=0x^2 + y^2 + 4x - 6y - 12 = 0

55

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