Line–circle intersections and chords · Short practice

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Recall

Line-circle intersections — objective 1

Maths4U Original · Short practice

The circle is \(\left(x - 22\right)^{2} + \left(y - 3\right)^{2} = 100\) and the line is \(\displaystyle y=9\).

Find the smaller intersection x-coordinate.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Line-circle intersections — objective 1

Maths4U Original · Short practice

The circle is \(\left(x - 23\right)^{2} + \left(y - 4\right)^{2} = 225\) and the line is \(\displaystyle y=13\).

Find the smaller intersection x-coordinate.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Method

Line-circle intersections — objective 2

Maths4U Original · Short practice

The circle is \(\left(x - 23\right)^{2} + \left(y - 4\right)^{2} = 225\) and the line is \(\displaystyle y=13\).

Find the larger intersection x-coordinate.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Line-circle intersections — objective 2

Maths4U Original · Short practice

The circle is \(\left(x - 24\right)^{2} + \left(y - 5\right)^{2} = 400\) and the line is \(\displaystyle y=17\).

Find the larger intersection x-coordinate.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

Line-circle intersections — objective 3

Maths4U Original · Short practice

The circle is \(\left(x - 24\right)^{2} + \left(y - 5\right)^{2} = 400\) and the line is \(\displaystyle y=17\).

Find the chord length.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Line-circle intersections — objective 3

Maths4U Original · Short practice

The circle is \(\left(x - 25\right)^{2} + \left(y - 6\right)^{2} = 25\) and the line is \(\displaystyle y=9\).

Find the chord length.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Check understanding

Line-circle intersections — objective 4

Maths4U Original · Short practice

The circle is \(\left(x - 25\right)^{2} + \left(y - 6\right)^{2} = 25\) and the line is \(\displaystyle y=9\).

Find the common y-coordinate of the intersections.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Line-circle intersections — objective 4

Maths4U Original · Short practice

The circle is \(\left(x - 26\right)^{2} + \left(y - 2\right)^{2} = 100\) and the line is \(\displaystyle y=8\).

Find the common y-coordinate of the intersections.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

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