A curved profile for a glass sculpture C C\,C is modeled by the parametric equations
x=14t2+1,y=2t−8t,t>0 x = \frac{1}{4}t^2 + 1, \quad y = 2t - \frac{8}{t}, \quad t > 0 x=41t2+1,y=2t−t8,t>0The curve C C\,C intersects the xxx-axis at the point QQQ.
Find the xxx-coordinate of QQQ.
The line l l\,l is the normal to C C\,C at the point PPP. Given that t=4t = 4t=4 at PPP:
Write down the coordinates of PPP.
Using calculus, show that an equation of l l\,l is
4x+5y=50 4x + 5y = 50 4x+5y=50The region R R\,R is bounded by the curve CCC, the line lll, and the xxx-axis.
Using algebraic integration, find the exact volume of the solid of revolution formed when the region R R\,R is rotated through 2π 2\pi\,2π radians about the xxx-axis.
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.