Summary of Chapter 2 (so far). Parallel lines  y = mx + c y = mx + d Perpendicular lines  y = mx + cy = nx + dm x n = -1 Length of a line using Pythagoras’

Slides:

Advertisements

Similar presentations

EXAMPLE 1 Write an equation of a line from a graph

Advertisements

Problem Set 2, Problem # 2 Ellen Dickerson. Problem Set 2, Problem #2 Find the equations of the lines that pass through the point (1,3) and are tangent.

Equation of Tangent line

Notes Over 10.3 r is the radius radius is 4 units

Coordinate Geometry – The Circle This week the focus is on solving problems which involve circles, lines meeting circles and lines and circles intersecting.

The Circle (x 1, y 1 ) (x 2, y 2 ) If we rotate this line we will get a circle whose radius is the length of the line.

1 OBJECTIVES : 4.1 CIRCLES (a) Determine the equation of a circle. (b) Determine the centre and radius of a circle by completing the square (c) Find the.

18: Circles, Tangents and Chords

Intersection of Loci You will be given a few conditions and asked to find the number of points that satisfy ALL the conditions simultaneously. The solution.

Starter Activity Write the equation of a circle with a center of

6.1 Use Properties of Tangents

Circles, Tangents and Chords

EXAMPLE 1 Write an equation of a line from a graph

Pupils notes for Circle Lessons.  The equation of a circle with centre ( a, b ) and radius r is We usually leave the equation in this form without multiplying.

Section 11.4 Areas and Lengths in Polar Coordinates.

Chapter 1 Functions, Graphs, and Limits. Copyright © Houghton Mifflin Company. All rights reserved.1 | 2 Figure 1.1: The Cartesian Plane.

Chapter 10.1 Notes: Use Properties of Tangents Goal: You will use properties of a tangent to a circle.

CIRCLE EQUATIONS The Graphical Form of the Circle Equation Inside, Outside or On the Circle Intersection Form of the Circle Equation Find intersection.

 The tangent theorem states that if two segments are tangent to a circle and intersect one another, the length from where the segments touch the circle.

The Second Degree Equations. Determine whether the following equations represent a circle, parabola, ellipse or hyperbola. 1. x 2 + 4y 2 – 6x + 10y.

Application of Derivative - 1 Meeting 7. Tangent Line We say that a line is tangent to a curve when the line touches or intersects the curve at exactly.

Circles Introduction Circle equation Circle properties Practice qs Points of intersection.

Writing & Identifying Equations of Parallel & Perpendicular Lines Day 94 Learning Target: Students can prove the slope criteria for parallel and perpendicular.

Higher Outcome 4 Higher Unit 2 The Graphical Form of the Circle Equation Inside, Outside or On the Circle.

Circles © Christine Crisp Objectives To know the equation of a circle (Cartesian form) To find the intersection of circles with straight lines To Find.

Section 3.2 Connections to Algebra.  In algebra, you learned a system of two linear equations in x and y can have exactly one solution, no solutions,

STROUD Worked examples and exercises are in the text PROGRAMME 8 DIFFERENTIATION APPLICATIONS 1.

Co-ordinate Geometry of the Circle Notes Aidan Roche 2009 Aidan Roche (c) Aidan Roche 2009.

Point Slope Form. Write the equation of the line with slope 3 and passing through the point (1, 5). y – y 1 = m(x – x 1 )

Section 3-5: Lines in the Coordinate Plane Goal 2.02: Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs.

The Equation of a Circle. Aims To recognise the equation of a circle To find the centre and radius of a circle given its equation To use the properties.

Curves & circles. Write down a possible equation that this could represent y = 6 – 3x or y = -3x + 6.

Next Quit Find the equation of the line which passes through the point (-1, 3) and is perpendicular to the line with equation Find gradient of given line:

Chord and Tangent Properties. Chord Properties C1: Congruent chords in a circle determine congruent central angles. ●

STROUD Worked examples and exercises are in the text Programme 9: Tangents, normals and curvature TANGENTS, NORMALS AND CURVATURE PROGRAMME 9.

Co-ordinate Geometry of the Circle

3.4 Parallel and Perpendicular Lines 1. Objectives  Understand the difference between parallel and perpendicular lines  Use the properties of parallel.

Warm Up 3-7 Write the standard form equation of the circle.

Circle Geometry.

Lecture 2 of 9 SECTIONS 1.2 CIRCLES CONIC.

SECTIONS Lecture 3 of CIRCLES CONIC.

Aim: How do we find points of intersection? What is slope? Do Now: Is the function odd, even or neither? 1)y - x² = 7 2)y = 6x - x⁷ 3)y = √ x⁴ - x⁶ 4)Find.

Straight Line Graph revision

Straight Line Graph revision

The equation of a circle

Chapter V. The Sphere 48. The equation of the sphere

Lesson 3-6: Perpendicular & Distance

Equations of Tangents.

Happy Chinese New Year Present

Co-ordinate Geometry for Edexcel C2

Chapter 1: Lesson 1.3 Slope-Intercept Form of a Line

Functions, Graphs, and Limits

Circle Centre (a, b) radius r

Chapter 13 Review White Boards!!!!.

The Circle x2+y2+2gx+2fy+c = 0 (x-a)2 + (y-b)2 = r2 x2 + y2 = r2

3.5 Write and Graph Equations of Lines

Chapter 3-6 Perpendiculars and Distance

Tangents to Circles.

The Point-Slope Form of the Equation of a Line

GCSE: Tangents To Circles

EXAMPLE 1 Write an equation of a line from a graph

Geometry Section 3.5.

Warm up Write an equation given the following information.

Warm up Write an equation given the following info:

3-4 Equations of Lines Forms of Equations

Parallel and Perpendicular Lines

Find and Use Slopes of Lines Write and Graph Equations of Lines

3.5 Write and Graph Equations of Lines

Presentation transcript:

Summary of Chapter 2 (so far)

Parallel lines  y = mx + c y = mx + d Perpendicular lines  y = mx + cy = nx + dm x n = -1 Length of a line using Pythagoras’ theorem Finding equation of a line when given coordinates and / or another line. Intersection of 2 lines by solving equations simultaneously Proofs about geometric properties Circles … intersection lines & curves or 2 curves

Centre (4,3) and radius of r – Equation of circle Choose any point on circle (x, y) Using Pythagoras (x – 4) 2 + (y – 3) 2 = r 2 From the diagram we can see that x = 6 and y = 6.4 (ish) (6 – 4) 2 + (6.4 – 3) 2 = r 2 r = 3.945

Centre (-2, 4) and radius of r. Passes through the point (1,8) Find the equation of the circle.

Question 5 … HINT! Show that x 2 + y 2 + 2x – 4y + 1 =0 Can be written as (x + 1) 2 + (y – 2) 2 = r 2 Exercise 2E – pg 67

Using geometric info (so far) If a circle has an equation of the form (x - h) 2 + (y - k) 2 = r 2 How would you find the equation of the tangent that meets the circle at (x, y)