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

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Equation of a Circle
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What is the centre of the circle (x+3)2+(y−2)2=17(x + 3)^2 + (y - 2)^2 = 17?

(−3,2)(-3, 2)

What is the radius of the circle (x−4)2+(y+3)2=72(x - 4)^2 + (y + 3)^2 = 72?

626\sqrt{2}

Find the centre of x2+y2+6x−4y−4=0x^2 + y^2 + 6x - 4y - 4 = 0 by completing the square.

(−3,2)(-3, 2)

What is the radius of x2+y2+3x−2y+1=0x^2 + y^2 + 3x - 2y + 1 = 0?

32\frac{3}{2}

A circle has centre (4,−3)(4, -3) and passes through (10,3)(10, 3). Find the radius.

626\sqrt{2}

Write the equation of a circle with centre (2,4)(2, 4) and radius 77 in standard form.

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

Expand (x−2)2+(y−4)2=49(x - 2)^2 + (y - 4)^2 = 49 to the form x2+y2+ax+by+c=0x^2 + y^2 + ax + by + c = 0.

x2+y2−4x−8y−29=0x^2 + y^2 - 4x - 8y - 29 = 0

For (x+a)2+(y+b)2=r2(x + a)^2 + (y + b)^2 = r^2, the centre is at which point?

(−a,−b)(-a, -b)

To find where circle x2+y2+6x−4y−4=0x^2 + y^2 + 6x - 4y - 4 = 0 meets y=3x+4y = 3x + 4, what do you do first?

Substitute y=3x+4y = 3x + 4 into circle eqn

What is the equation of a circle centred at the origin with radius rr?

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

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