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SingaporeAdditional MathematicsQuick questions
Coordinate Geometry and Circles
Quick questions on Lines and circles together explained: O-Level A-Maths
7short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What are finding intersection points?Show answer
To find where a line meets a circle, substitute the line's equation into the circle's equation. This gives a quadratic in one variable whose solutions are the -coordinates (or -coordinates) of the intersection points; back-substitute into the line to find the partners.
What is the tangent at a point of contact?Show answer
A tangent touches the circle at exactly one point and is perpendicular to the radius drawn to that point. So:
What is the perpendicular-radius shortcut?Show answer
Because the radius to the point of contact is perpendicular to the tangent, the perpendicular distance from the centre to a tangent line equals the radius. This gives a second way to test or find tangents without the discriminant.
What is tangent gradient without the negative reciprocal?Show answer
The tangent is perpendicular to the radius, so use the negative reciprocal of the radius gradient.
What is q1?Show answer
Find where the line meets the circle . [3 marks]
What is q2?Show answer
State the tangent gradient to a circle centre at the point . [2 marks]
What is q3?Show answer
Determine whether meets the circle . [3 marks]
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