Circle with Centre other than (0,0) (Leaving Cert Mathematics): Quizzes

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Circle with Centre other than (0,0)
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What is a circle defined as?

Points equidistant from a centre

In the equation (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2, what does (h,k)(h, k) represent?

Centre of the circle

In the equation (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2, what does rr represent?

Radius of the circle

What is the equation of a circle with centre (3,−2)(3, -2) and radius 55?

(x−3)2+(y+2)2=25(x - 3)^2 + (y + 2)^2 = 25

What is the centre of the circle (x−4)2+(y+1)2=9(x - 4)^2 + (y + 1)^2 = 9?

(4,−1)(4, -1)

What is the radius of the circle (x−2)2+(y+3)2=16(x - 2)^2 + (y + 3)^2 = 16?

44

What is the standard form of a circle's equation?

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

How do you verify if a point lies on a circle?

Substitute coordinates into equation

Is point (6,2)(6, 2) on circle (x−3)2+(y+2)2=25(x - 3)^2 + (y + 2)^2 = 25?

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

What does rr represent in terms of distance?

Fixed distance from centre to circle

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The Circle

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The Basics

Points Inside, Outside or On a Circle

Intersection of a Line and a Circle

Tangents & Touching Circles

Problems in g, f and c

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The Circle

The Basics

Points Inside, Outside or On a Circle

Intersection of a Line and a Circle

Tangents & Touching Circles

Problems in g, f and c

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