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1.3 Coordinate Geometry in the x-y Plane

1.3 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]
Markscheme

1.3 Coordinate Geometry in the x-y Plane Questions

  1. A Level
  2. /Maths
  3. /1.3 Coordinate Geometry in the x-y Plane

143 exam-style questions on OCR A Level Maths 1.3 Coordinate Geometry in the x-y Plane, covering 1.3.1 Straight lines, 1.3.2 Parallel and perpendicular lines, 1.3.3 Straight line models, 1.3.4 Coordinate geometry of a circle, 1.3.5 Centre and radius by completing the square, 1.3.6 Circle properties, 1.3.7 Parametric equations of curves (A-level only), 1.3.8 Parametric equations in context (A-level only), and 1.3 Coordinate Geometry in the x-y Plane. Each one has a worked solution and a mark scheme showing where the marks go.

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