A Circle Intersecting the Axes (Leaving Cert Mathematics): Quizzes

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A Circle Intersecting the Axes
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To find where a circle intersects the x-axis, what value should you substitute?

y=0y = 0

To find where a circle intersects the y-axis, what value should you substitute?

x=0x = 0

What form do x-axis intersection points always take?

(x,0)(x, 0)

What form do y-axis intersection points always take?

(0,y)(0, y)

Where does x2+y2=16x^2 + y^2 = 16 intersect the x-axis?

(4,0)(4, 0) and (−4,0)(-4, 0)

Where does (x+3)2+(y−2)2=10(x + 3)^2 + (y - 2)^2 = 10 intersect the y-axis?

(0,1)(0, 1) and (0,3)(0, 3)

How many points does a circle intersect an axis when it is tangent to that axis?

Exactly one point

For a circle with centre (a,b)(a, b) and radius rr tangent to the x-axis, which is true?

∣b∣=r|b| = r

For a circle with centre (a,b)(a, b) and radius rr tangent to the y-axis, which is true?

∣a∣=r|a| = r

Why must you include ± when taking square roots to find intersections?

Circles usually intersect axes at 2 points

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