Co-ordinate Geometry 2 25 th November 2019 Welcome! Coordinate - PowerPoint PPT Presentation

Co-ordinate Geometry 2 25 th November 2019

Welcome! • Coordinate Geometry – 1. The Line – Key Concepts Revision 2. Circle • Question Focused Approach • 1.5 hours - 10mins break @7pm • Any questions? – Just Ask!!

Useful Resource for Project Maths • www.themathstutor.ie • Normally €99.99 • Discount code: SAI • €49.50 for the year • Access only to June 2019

Material from tonight • Slides, questions and solutions available from website: https://web.actuaries.ie/students/tutorials • Or google ‘actuaries maths tutorials’ to find it.

Exam Technique: • Read the question carefully. • Key formula tables – page 18 & 19. • Know your theorems. • Draw a diagram every time. • Label all diagrams. • Write down your workings. • Is your result plausible?

Line y k B(x 2 ,y 2 ) y 2 -y 1 A(x 1 ,y 1 ) x 2 -x 1 O x A(x 1 ,y 1 ) and B(x 2 ,y 2 ) are points on a line k. The slope m = (y 2 -y 1 )/(x 2 -x 1 ) Given two points A(x 1 ,y 1 ) and B(x 2 ,y 2 ), or given one point A(x 1 ,y 1 ) and the slope m, (𝑧−𝑧 1 ) (𝑧 2 −𝑧 1 ) (𝑧−𝑧 1 ) (𝑦−𝑦 1 ) = (𝑦 2 −𝑦 1 ) [= m] or (𝑦−𝑦 1 ) = m equation of line:

Line y y = mx + c c O x The equation of the line can be written in the form: y = mx + c (c the intercept on the y-axis, where x=0) m can be positive (concave angle with x-axis) or negative (convex angle with x-axis). Lines with same slope are parallel. Lines with slopes m and -1/m are perpendicular. The equation of the line can also be written in the form ax+by+c = 0 (for use in formulae)

Circle (x,y) Centre (h,k) Radius r r y-k (h,k) x-h (x-h) 2 + (y-k) 2 = r 2

Circle • Key formulae – page 19 Find inding th the e eq equation of of a a ci circle:  (𝑦 − ℎ) 2 +(𝑧 − 𝑙) 2 = 𝑠 2 F ormula for circle with centre (h, k)  𝑦² + 𝑧² = 𝑠² F ormula for circle with centre (0, 0) Find inding th the e cen centre an and rad adius of of a a ci circle:  Express the circle in this form: 𝑦 2 + 𝑧 2 + 2𝑕𝑦 + 2𝑔𝑧 + 𝑑 = 0  Centre of the circle is (-g, -f)  Radius of the circle is √(g 2 + f 2 – c)

Circle The The pe perpe pendicular bi bisector of of an any ch chord is is a a lin line co containing th the cen centre of of th the ci circle

Next tutorial • Monday 2 nd December • Trigonometry 2 • Same location • 6 - 8 pm • https://web.actuaries.ie/students/tutorials