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AS Unit 1 Pure Mathematics A

Quick questions on Coordinate geometry: straight lines and circles - WJEC A-Level Maths

4short 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 equation of a circle?
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A circle with centre (a,b)(a, b) and radius rr has equation (x−a)2+(y−b)2=r2(x-a)^2 + (y-b)^2 = r^2. When given in expanded form x2+y2+Dx+Ey+F=0x^2 + y^2 + Dx + Ey + F = 0, complete the square in xx and yy to recover the centre and radius.
What is q1?
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Find the equation of the line through (2,−1)(2, -1) perpendicular to y=3x+4y = 3x + 4. [3 marks]
What is q2?
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A circle has centre (2,−3)(2, -3) and passes through (5,1)(5, 1). Find its equation. [3 marks]
What is q3?
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Show that the line y=2x−5y = 2x - 5 is a tangent to the circle x2+y2=5x^2 + y^2 = 5. [3 marks]

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