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

Slides:

Advertisements

Similar presentations

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.

Advertisements

Equation of Tangent line

Tangents and Circles. Tangent Definition A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point.

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.

The Power Theorems Lesson 10.8

Circles Write an equation given points

Circles – Tangent Lines A tangent line touches a circle at exactly one point. In this case, line t is tangent to circle A. t A.

Given three points of a circle: (-1,1), (7,-3), (-2,-6).

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.

Lesson 8-6: Segment Formulas

Terminal Arm Length and Special Case Triangles DAY 2.

Higher Maths Question Types. Functions & Graphs TYPE questions (Trig, Quadratics) Sketching Graphs Composite Functions Steps : 1.Outside function stays.

1 Lesson 10.6 Segment Formulas. 2 Intersecting Chords Theorem A B C D E Interior segments are formed by two intersecting chords. If two chords intersect.

Quadratic Theory Introduction This algebraic expression: x 2 + 2x + 1 is a polynomial of degree 2 Expressions like this in which the highest power of x.

EXAMPLE 1 Graph an equation of a circle

Circles, Tangents and Chords

Midpoint formula: Distance formula: (x 1, y 1 ) (x 2, y 2 ) 1)(- 3, 2) and (7, - 8) 2)(2, 5) and (4, 10) 1)(1, 2) and (4, 6) 2)(-2, -5) and (3, 7) COORDINATE.

Circles Notes. 1 st Day A circle is the set of all points P in a plane that are the same distance from a given point. The given distance is the radius.

Higher Supported Study

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.

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

Warm-Up Find the area and circumference of a circle with radius r = 4.

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

Section 6.2 – The Circle. Write the standard form of each equation. Then graph the equation. center (0, 3) and radius 2 h = 0, k = 3, r = 2.

Warm-Up Find the distance and the midpoint. 1. (0, 3) and (3, 4)

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.

Higher Maths 2 4 Circles1. Distance Between Two Points 2Higher Maths 2 4 Circles The Distance Formula d =d = ( y2 – y1)²( y2 – y1)² + ( x2 – x1)²( x2.

Co-ordinate Geometry of the Circle

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’

Circles Formula. x 2 + y 2 = r 2 Formula for Circle centered at the origin Center point (0,0) Radius = r.

Warm Up Find the slope of the line that connects each pair of points. – (5, 7) and (–1, 6) 2. (3, –4) and (–4, 3)

10.3 Circles 10.3 Circles What is the standard form equation for a circle? Why do you use the distance formula when writing the equation of a circle? What.

SECTIONS Lecture 3 of CIRCLES CONIC.

10-6 Find Segment Lengths in Circles. Segments of Chords Theorem m n p m n = p q If two chords intersect in the interior of a circle, then the product.

Straight lines tangent to circles. Find the perpendicular bisector between the centres Draw arc from bisector through centres.

Beat the Computer Drill Equation of Circle

Recognise and use x2 + y2 = r2

Co-ordinate Geometry in the (x, y) Plane.

Chapter 10: Properties of Circles

Geometry Revision contd.

Section 10.1 – The Circle.

Notes Over 10.3 r is the radius radius is 4 units

Co-ordinate Geometry for Edexcel C2

COORDINATE PLANE FORMULAS:

10.6 Equations of Circles Geometry.

Lesson 8-6: Segment Formulas

f(x) = a(x + b)2 + c e.g. use coefficients to

t Circles – Tangent Lines

Graph and Write Equations of Circles

Tangents to Circles A line that intersects with a circle at one point is called a tangent to the circle. Tangent line and circle have one point in common.

Circle Centre (a, b) radius r

r > 0 Does circles touch externally or internally ? radius = (a,b)

Circles Tools we need for circle problems:

Lesson 8-6: Segment Formulas

Chapter 3-6 Perpendiculars and Distance

9.3 Graph and Write Equations of Circles

Tangents to Circles.

Segments of Chords, Secants & Tangents Lesson 12.7

Lesson 8-6: Segment Formulas

Lesson 8-6 Segment Formulas.

28. Writing Equations of Circles

Lesson 10-7: Segment Formulas

Lesson 8-6: Segment Formulas

Tangents to Circles Advanced Geometry.

Presentation transcript:

The Circle x2+y2+2gx+2fy+c = 0 (x-a)2 + (y-b)2 = r2 x2 + y2 = r2 Graph Sketching b2 - 4ac < 0 2 pts of intersection Move the circle from the origin a units to the right b units upwards Used for intersection problems between circles and lines Factorisation b2 - 4ac < 0 No intersection x2+y2+2gx+2fy+c = 0 Centre (a,b) Centre (-g,-f) b2 - 4ac = 0 1 pt of intersection TANGENT to circle The Circle (x-a)2 + (y-b)2 = r2 Straight line Theory Pythagoras Theorem rotated through 360o x2 + y2 = r2 Perpendicular Equation m1xm2 = -1 Two circles touch externally if the distance C1C2=(r1 + r2) Distance Formula Two circles touch internally if the distance C1C2=(r1 - r2) Centre (0,0)