Equation of a Circle: Centre at (a;b) (Grade 12 NSC Matric Mathematics): Quizzes

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Equation of a Circle: Centre at (a;b)
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What is the standard form equation of a circle with centre (a;b)(a; b) and radius rr?

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

What is the centre of the circle (x−3)2+(y+4)2=9(x - 3)^2 + (y + 4)^2 = 9?

(3;−4)(3; -4)

What is the radius of the circle (x+1)2+(y−2)2=16(x + 1)^2 + (y - 2)^2 = 16?

4 units

What is the equation of a circle with centre at the origin and radius 4?

x2+y2=16x^2 + y^2 = 16

A circle x2+y2=25x^2 + y^2 = 25 shifts 3 units right. What replaces xx in the new equation?

(x−3)(x - 3)

When completing the square for x2+6xx^2 + 6x, what value is added and subtracted?

9

Circle with centre C(2;−3)C(2; -3) passes through P(2;1)P(2; 1). What is r2r^2?

16

In the equation (x−5)2+(y−2)2=9(x - 5)^2 + (y - 2)^2 = 9, what is the x-coordinate of the centre?

5

Points A(−2;3)A(-2; 3) and B(−2;−5)B(-2; -5) are diameter endpoints. What is the centre?

(−2;−1)(-2; -1)

Two circles touch externally. What is the relationship between distance dd and radii?

d=r1+r2d = r_1 + r_2

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