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SingaporeAdditional MathematicsQuick questions

Coordinate Geometry and Circles

Quick questions on The equation of a circle explained: O-Level A-Maths

6short 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 is the general form?
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Expanding the standard form gives the general equation:
What is testing whether a point lies on the circle?
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Substitute the point into the equation: if it satisfies (x−a)2+(y−b)2=r2(x - a)^2 + (y - b)^2 = r^2, the point is on the circle. If the left side is less than r2r^2 the point is inside, and if greater it is outside, which is a quick way to classify a location relative to a circular boundary.
What is negative radius squared?
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If g2+f2−cg^2 + f^2 - c is negative, no real circle exists; check before taking the root.
What is q1?
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State the centre and radius of (x−2)2+(y+5)2=9(x - 2)^2 + (y + 5)^2 = 9. [2 marks]
What is q2?
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Write the equation of the circle with centre (0,0)(0, 0) and radius 77. [1 mark]
What is q3?
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Find the centre and radius of x2+y2+2x−8y+1=0x^2 + y^2 + 2x - 8y + 1 = 0. [3 marks]

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