Analytical Geometry (Grade 12 NSC Matric Mathematics): Quizzes

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Equation of a Circle: Centre at Origin
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What defines a circle?

Points equidistant from centre

What is true about the radius of a circle?

Distance from centre remains constant

If a circle has radius r=4r = 4 units, what is the diameter?

88 units

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

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

A circle has centre O(0; 0) and radius 5. What is its equation?

x2+y2=25x^2 + y^2 = 25

Does point (3; 4) lie on the circle x2+y2=25x^2 + y^2 = 25?

Yes, 32+42=253^2 + 4^2 = 25

A circle with centre O(0; 0) passes through (-5; 5). Find r2r^2.

5050

If (x; y) lies on a circle centred at origin, which point also lies on it?

(−x;−y)(-x; -y)

On circle x2+y2=45x^2 + y^2 = 45, find y when x=2yx = 2y and y>0y > 0.

y=3y = 3

Points P(-5; 5) and Q(5; -5) lie on circle centre O(0; 0). Is PQ a diameter?

Yes, opposite through origin

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