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Practice — Coordinate Geometry • The equation of a circle

Centre, radius
Difficulty: ★☆☆
16
Determine the centre and radius: \( (x-2)^2+(y+1)^2=9\)
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Centre, radius
Difficulty: ★☆☆
17
Determine the centre and radius of the circle: \( (x+3)^2+(y-8)^2=36\)
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Centre, radius
Difficulty: ★☆☆
18
Determine the centre and radius of the circle: \( (x+5)^2+(y+6)^2=1\)
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Centre
Difficulty: ★★☆
19
Determine the coordinates of the centre: \( x^2 + y^2 - 6x + 8y + 10 = 0 \)
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Centre, radius
Difficulty: ★★☆
20
Determine the centre and radius: \( x^2 + y^2 - x - 10y + 5 = 0 \)
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Centre
Difficulty: ★★☆
21
Dtermine the coordinates of the centre: \( 2x^2 + 2y^2 - 8x + 2y + 2 = 0 \)
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Circle equations and tangents: check 1
Difficulty: ★★☆
2273
Info
M4U-P1-QP-COORDINATE-GEOMETRY-CIRCLES-01

Maths4U Original · Short practice

Find the radius of \((x-4)^2+(y+2)^2=49\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

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Circle equations and tangents: check 2
Difficulty: ★★☆
2274
Info
M4U-P1-QP-COORDINATE-GEOMETRY-CIRCLES-02

Maths4U Original · Short practice

Find the x-coordinate of the centre of \(x^2+y^2-6x+8y=0\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

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Circle equations and tangents: check 3
Difficulty: ★★☆
2275
Info
M4U-P1-QP-COORDINATE-GEOMETRY-CIRCLES-03

Maths4U Original · Short practice

A circle has diameter endpoints \((-2,1)\), \((4,9)\). Find its radius.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

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Circle equations and tangents: check 4
Difficulty: ★★☆
2276
Info
M4U-P1-QP-COORDINATE-GEOMETRY-CIRCLES-04

Maths4U Original · Short practice

The circle \(x^2+y^2=25\) has tangent at \((3,4)\). Which equation is that tangent?

Choose one answer.

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Circle equations and tangents: check 5
Difficulty: ★★☆
2427
Info
M4U-P1-QP-COORDINATE-GEOMETRY-CIRCLES-05

Maths4U Original · Short practice

AB is a diameter of a circle and C is a different point on that circle. What is angle ACB?

Choose one answer.

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Circle equations and tangents: review variant 1
Difficulty: ★★☆
2483
Info
M4U-P1-QP-VAR-COORDINATE-GEOMETRY-CIRCLES-01

Maths4U Original · Short practice

Find the radius of \((x+3)^2+(y-1)^2=36\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

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Circle equations and tangents: review variant 2
Difficulty: ★★☆
2484
Info
M4U-P1-QP-VAR-COORDINATE-GEOMETRY-CIRCLES-02

Maths4U Original · Short practice

Find the centre x-coordinate of \(x^2+y^2+4x-10y+4=0\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

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Circle equations and tangents: review variant 3
Difficulty: ★★☆
2485
Info
M4U-P1-QP-VAR-COORDINATE-GEOMETRY-CIRCLES-03

Maths4U Original · Short practice

A diameter has endpoints \((0,0)\), \((10,24)\). Find the radius.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

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Circle equations and tangents: review variant 4
Difficulty: ★★☆
2486
Info
M4U-P1-QP-VAR-COORDINATE-GEOMETRY-CIRCLES-04

Maths4U Original · Short practice

Find the tangent gradient to \(x^2+y^2=25\) at \((4,3)\).

Enter one number or fraction. Round decimals to at least six decimal places when needed.

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Circle equations and tangents: review variant 5
Difficulty: ★★☆
2487
Info
M4U-P1-QP-VAR-COORDINATE-GEOMETRY-CIRCLES-05

Maths4U Original · Short practice

AB is a circle diameter. C is another point on the circle. If angle ABC is \(28^\circ\), find angle BAC in degrees.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

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