Points and Circles (Leaving Cert Mathematics): Flashcards

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Points and Circles
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What are the three possible positions of a point relative to a circle?

Inside, on, outside

Point inside circle: distance from centre vs radius

Distance < radius

Point on circle: distance from centre vs radius

Distance = radius

Point outside circle: distance from centre vs radius

Distance > radius

Distance formula between (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2)

d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Standard circle equation (centre at origin)

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

If x2+y2=kx^2 + y^2 = k, what is rr?

r=kr = \sqrt{k}

Substitution method: if x2+y2<r2x^2 + y^2 < r^2, point is...

Inside the circle

Substitution method: if x2+y2=r2x^2 + y^2 = r^2, point is...

On the circle

Substitution method: if x2+y2>r2x^2 + y^2 > r^2, point is...

Outside the circle

Fastest method for circles centred at origin

Substitution method

Method that works for all circle equations

Distance comparison method

Explore Leaving Cert Mathematics Revision Notes by Topics

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

Explore Leaving Cert Mathematics Model Answers by Topics

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

Explore Leaving Cert Mathematics Quizzes by Topics

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

Explore Leaving Cert Mathematics Exam Questions by Topics

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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