A micro-robotic probe's position (x,y)(x, y)(x,y) in micrometres is tracked over time t t\,t seconds within a biological medium. The path is defined by the parametric equations
x=4×2−t−1 x = 4 \times 2^{-t} - 1 x=4×2−t−1 y=3×2t+5 y = 3 \times 2^{t} + 5 y=3×2t+5Show that dydx=−34×22t\dfrac{dy}{dx} = -\dfrac{3}{4} \times 2^{2t}dxdy=−43×22t.
Find the Cartesian equation of the curve in the form xy+ax+by=cxy + ax + by = cxy+ax+by=c, where aaa, bbb and ccc are integers.
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.