Recall · M4U-P1-QP-COORDINATE-GEOMETRY-LINE-CIRCLE-01
secant
Maths4U Original · Short practice
How many intersections do \(y=3\) and \(x^2+y^2=25\) have?Enter one number or fraction. Round decimals to at least six decimal places when needed.
Pure 1 course · All short practice · Notes & examples
Maths4U Original · 9709 Pure 1
Line–circle intersections, chords and tangency
Check a short answer, use a hint, then study the reasoning. These checks assess the final answer; use the exam-style problems to practise written explanations.
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Method · M4U-P1-QP-COORDINATE-GEOMETRY-LINE-CIRCLE-02
chord length
Maths4U Original · Short practice
Find the length of the chord cut by \(y=3\) on \(x^2+y^2=25\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Apply · M4U-P1-QP-COORDINATE-GEOMETRY-LINE-CIRCLE-03
no intersection
Maths4U Original · Short practice
How does \(y=6\) meet \(x^2+y^2=25\)?Choose one answer.
Check understanding · M4U-P1-QP-COORDINATE-GEOMETRY-LINE-CIRCLE-04
tangency condition
Maths4U Original · Short practice
The line \(y=k\), with \(k>0\), is tangent to \(x^2+y^2=36\). Find \(k\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-COORDINATE-GEOMETRY-LINE-CIRCLE-01
secant
Maths4U Original · Short practice
How many intersections do \(y=6\), \(x^2+y^2=36\) have?Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-COORDINATE-GEOMETRY-LINE-CIRCLE-02
chord length
Maths4U Original · Short practice
Find the chord length cut by \(y=12\) on \(x^2+y^2=169\).Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-COORDINATE-GEOMETRY-LINE-CIRCLE-03
no intersection
Maths4U Original · Short practice
How many real intersections do \(x=7\), \(x^2+y^2=64\) have?Enter one number or fraction. Round decimals to at least six decimal places when needed.
Fresh review variant · M4U-P1-QP-VAR-COORDINATE-GEOMETRY-LINE-CIRCLE-04
tangency condition
Maths4U Original · Short practice
The line \(y=k\), k positive, is tangent to \(x^2+y^2=81\). Find k.Enter one number or fraction. Round decimals to at least six decimal places when needed.