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1.6 C: Coordinate geometry in the (x, y) plane

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Question 2

A circle C C\,C has centre (10,6)(10, 6)(10,6) and radius 2172\sqrt{17}217​. A line L L\,L has equation y=mxy = mxy=mx.

a.

Show that the xxx-coordinate of any points of intersection of C C\,C and L L\,L satisfies the equation (m2+1)x2−(12m+20)x+68=0(m^2 + 1)x^2 - (12m + 20)x + 68 = 0(m2+1)x2−(12m+20)x+68=0.

[4]
b.

Find values of m m\,m for which the equation in (a) has equal roots.

[4]
c.

Two lines drawn from the origin which are tangents to CCC. Find the coordinates of the points of contact between the tangents and CCC.

[4]

1.6 C: Coordinate geometry in the (x, y) plane Questions

  1. A Level
  2. /Maths
  3. /1.6 C: Coordinate geometry in the (x, y) plane

Practise AQA A Level Maths 1.6 C: Coordinate geometry in the (x, y) plane with exam-style questions for A Level Maths. 110 questions covering 1.6.1 Equation of a straight line, 1.6.2 Coordinate geometry of the circle, 1.6.3 Parametric equations of curves (A-level only), and 1.6.4 Parametric equations in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank