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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 7

The curve $C\,$ has parametric equations

$x = 2 t$ , $y = t^2 - k$

where $k\,$ is a positive constant.

$C\,$ meets the line $y = x$ at two points, $A\,$ and $B$ .

a.

Show that the $x$ -coordinates of $A\,$ and $B\,$ satisfy

$x^2 - 4x - 4k = 0$

[3]

b.

Given that the length of $AB\,$ is $50\sqrt{50}$ , find the value of $k$ .

[5]

Markscheme

1.3 Coordinate Geometry in the x-y Plane Questions

A Level
Maths
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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