Circles HW #1.

Slides:

Advertisements

Similar presentations

Equation of Tangent line

Advertisements

10.1 Tangents to Circles.

10.1 Use Properties of Tangents

Lesson 6.1 Properties of Tangents Page 182. Q1 Select A A.) This is the correct answer. B.) This is the wrong answer. C.) This is just as wrong as B.

Definitions A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. Radius – the distance.

Tangents, Arcs, and Chords

Objectives Write an equation for a circle.

10.1 Use Properties of Tangents.  Circle - the set of all points in a plane that are equidistant from a given point.  Center - point in the middle of.

Circles 10-2 Warm Up Lesson Presentation Lesson Quiz Holt Algebra2.

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.

Tangents to Circles Pg 595. Circle the set of all points equidistant from a given point ▫Center Congruent Circles ▫have the same radius “Circle P” or.

Geometry Honors Section 9.5 Segments of Tangents, Secants and Chords.

Tangency. Lines of Circles EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord,

Section 12.1: Lines That intersect Circles

Circles Write an equation given points

Section 10 – 1 Use Properties of Tangents. Vocabulary Circle – A set of all points that are equidistant from a given point called the center of the circle.

CIRCLES Chapter 10.

Ch 11 mini Unit. LearningTarget 11-1 Tangents I can use tangents to a circle to find missing values in figures.

12-1 Tangent Lines. Definitions A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point called the.

[x – (–8)] 2 + (y – 0) 2 = ( 5 ) 2 Substitute (–8, 0) for (h, k) and 5 for r. Write the standard equation of a circle with center (–8, 0) and radius 5.

6.1 Use Properties of Tangents

Section 10.1 cont. Tangents. A tangent to a circle is This point of intersection is called the a line, in the plane of the circle, that intersects the.

EXAMPLE 1 Graph an equation of a circle

Geometry Honors Section 9.2 Tangents to Circles. A line in the plane of a circle may or may not intersect the circle. There are 3 possibilities.

EXAMPLE 4 Write a circular model Cell Phones A cellular phone tower services a 10 mile radius. You get a flat tire 4 miles east and 9 miles north of the.

EXAMPLE 1 Graph an equation of a circle Graph y 2 = – x Identify the radius of the circle. SOLUTION STEP 1 Rewrite the equation y 2 = – x

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

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.

Definitions  Circle: The set of all points that are the same distance from the center  Radius: a segment whose endpoints are the center and a point.

Introduction to Conic Sections

Graphs and Equations of Circles (might want some graph paper) Book: Math 3 (Green Book) Section: 5.2 Circles Quiz: Thursday Circles Test: Sept. 17.

9.1 Introduction to Circles. Some definitions you need Circle – set of all points in a plane that are equidistant from a given point called a center of.

Bell work What is a circle?. Bell work Answer A circle is a set of all points in a plane that are equidistant from a given point, called the center of.

Section 9.1 Basic terms of Circles Circles. What is a circle? Circle: set of points equidistant from the center Circle: set of points equidistant from.

Section 10-1 Tangents to Circles. Circle The set of all points in a plane that are equidistant from a given point (center). Center Circles are named by.

EXAMPLE 1 Graph an equation of a circle

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

Use Properties of Tangents

Properties of Tangents. EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter,

Pg 651. A chord is a line segment with each endpoint on the circle A diameter is a chord that passes through the center of the circle. A secant of a circle.

Lesson 11.1 Parts of a Circle Pages Parts of a Circle A chord is a segment whose endpoints are points on a circle. A diameter is a chord that.

TISK & 2 MM Lesson 9-5: Tangents Homework: 9-5 problems in packet 2 Monday, February 11, 2013 Agenda

EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent.

Circles Chapter 12.

Chapter 10 Circles Section 10.1 Goal – To identify lines and segments related to circles To use properties of a tangent to a circle.

Unit 1 – Conic Sections Section 1.2 – The Circle Calculator Required.

Circles 5.3 (M3). EXAMPLE 1 Graph an equation of a circle Graph y 2 = – x Identify the radius of the circle. SOLUTION STEP 1 Rewrite the equation.

Warm Up Week 1. Section 10.1 Day 1 I will identify segments and lines related to circles. Circle ⊙ p Circle P P.

9-5 Tangents Objectives: To recognize tangents and use properties of tangents.

10.1 Use Properties of Tangents

Chapter 14: CIRCLES!!! Proof Geometry.

Holt Algebra Circles 10-2 Circles Holt Algebra2 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

10.1 Tangent Properties to a Circle. POD 1. What measure is needed to find the circumference or area of a circle? 2. Find the radius of a circle with.

Sect Circles in the Coordinate Plane Geometry Honors.

Sect Tangents to Circles

Chords, secants and tangents

Introduction to Graphing

Graph and Write Equations of Circles

Section 10.1 Tangents to Circles.

Graph and Write Equations of Circles

Chapter 1 Graphs, Functions, and Models.

9.3 Graph and Write Equations of Circles

Trigonometry Chapter 9 Section 1.

EXAMPLE 1 Identify special segments and lines

Segment Lengths in Circles

Warm Up Complete the square and write as a squared binomial.

Section 10-1 Tangents to Circles.

Presentation transcript:

Circles HW #1

Complete the square and write as a squared binomial. 1. x2 + 6x + _____ = _____________ 2. x2 – 10x + _____ = _____________ 3. x2 + 24x + _____ = _____________ 4. x2 + 2x + _____ = _____________ 5. x2 – 5x + _____ = ______________ 6. This will be a critical skill we will use later on with conic sections!

Solve by completing the square: x2 + 6x – 16 = 0 x2 – 4x = 11

Write the equation in standard form for the given circle:

Lines Tangent to Circles Section: 5.2 (Green Book) Circles Quiz: Thursday Circles Test: Sept. 17

What we should know already: Chord: A line segment whose endpoints are on the circle Secant: A line that intersects the circle in two points Radius: The distance from the center to a point on the circle

What we should know already: Diameter: A chord that passes through the center of the circle Tangent: A line in the plane of a circle that intersects the circle in EXACTLY one point

Helpful Theorems If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency

Helpful Theorems In a plane, if a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle.

If two lines are Perpendicular… What do we know about their slopes? Their slopes are opposite reciprocals to each other!!!!!!!! Let’s use this to find some tangents….

Find an equation of the line tangent to the given circle at the given point What’s the slope of the radius to point (-1, 3)? So……..

Slope of Tangent The slope of the tangent must be the opposite reciprocal of -3, which is

Writing the Equation Point Slope Form: So to write the equation of our tangent line:

OR You can use Slope-Intercept form: y = 1/3x + b  plug in the point,(-1, 3) to find b

Find an equation of the line tangent to the given circle at the given point (x – 3)2 + (y + 2)2 = 130 at point (-4, 7)

Write a circular model Cell Phones A cellular phone tower services a 10 mile radius. You get a flat tire 4 miles east and 9 miles north of the tower. Are you in the tower’s range? SOLUTION In the diagram above, the origin represents the tower and the positive y-axis represents north. STEP 1 Write an inequality for the region covered by the tower. From the diagram, this region is all points that satisfy the following inequality: x2 + y2 < 102

Write a circular model continued…. STEP 2 Substitute the coordinates (4, 9) into the inequality from Step 1. x2 + y2 < 102 Inequality from Step 1 42 + 92 < 102 ? Substitute for x and y. 97 < 100  The inequality is true. ANSWER So, you are in the tower’s range.

HOMEWORK Circle Homework #2 WS