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1.5 Coordinate Geometry

1.5 Coordinate Geometry

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Question 88

A curve C C\,C is defined by the equation

x=3tan⁡(y+π3)x∈R,−5π6<y<π6 x = 3\tan\left(y + \frac{\pi}{3}\right) \quad x \in \mathbb{R}, \quad -\frac{5\pi}{6} < y < \frac{\pi}{6} x=3tan(y+3π​)x∈R,−65π​<y<6π​
a.

Show that

dydx=ax2+b \frac{dy}{dx} = \frac{a}{x^2 + b} dxdy​=x2+ba​

where a a\,a and b b\,b are integers to be determined.

[4]
b.

The point P P\,P on C C\,C has yyy-coordinate −π12\displaystyle -\frac{\pi}{12}−12π​. The tangent to C C\,C at P P\,P intersects the xxx-axis at the point QQQ. Determine the exact xxx-coordinate of QQQ.

[5]
Markscheme

1.5 Coordinate Geometry Questions

  1. A Level
  2. /Maths
  3. /1.5 Coordinate Geometry

178 exam-style questions on OCR (MEI) A Level Maths 1.5 Coordinate Geometry, covering 1.5.1 Equation of a straight line y = mx + c, 1.5.2 Gradients of parallel and perpendicular lines, 1.5.3 Distance between two points, 1.5.4 Midpoint of a line segment, 1.5.5 Form the equation of a straight line, 1.5.6 Draw a line given its equation, 1.5.7 Point of intersection of two lines, 1.5.8 Straight line models, 1.5.9 Intersection of a line and a curve, 1.5.10 Intersection of a line and a circle, 1.5.11 Equation of a circle, 1.5.12 Circle properties, 1.5.13 Parameter and parametric equations (A-level only), 1.5.14 Convert between cartesian and parametric forms (A-level only), 1.5.15 Equation of a circle in parametric form (A-level only), 1.5.16 Gradient of a parametric curve (A-level only), 1.5.17 Parametric equations in modelling (A-level only), and 1.5 Coordinate Geometry. Each one has a worked solution and a mark scheme showing where the marks go.

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