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.

Slides:



Advertisements
Similar presentations
Objectives Write equations and graph circles in the coordinate plane.
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.
Objectives Write an equation for a circle.
Circles Write an equation given points
Circles.
CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula.
Circles Date: _____________.
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.
Distance and Midpoint Formulas; Circles
 What is the equation of the line, in slope- intercept form, that passes through (2, 4) and is perpendicular to 5x+7y-1=0.
Circles Lesson Describe what each of the following equations make: 1.y = 4 2.3x + 2y = x 2 – 6x + 12 = 0 4.x 2 + y 2 = 9 1.Horizontal line.
Homework: p ,3,7,15,19 21,27,31,33,37,41,43,49,53,55,57.
Keystone Geometry Unit 7
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.
CIRCLES Topic 7.3.
Geometry Equations of a Circle.
Equations of Circles.
Warm up O Find the coordinates of the midpoint of the segment that has endpoints at (- 5, 4) and (7, - 2). O Find the distance between points at (10,
Introduction to Conic Sections
Distance and Midpoint Graphing, Symmetry, Circles Solving.
Do Now!!! Find the values of x that satisfy and explain how you found your solution. Solution: First, you must factor the numerator and denominator if.
10.1– Use Properties of Tangents of Circles. TermDefinitionPicture Circle The set of all points in a plane that are equidistant from a given point.
10.1 – Tangents to Circles. A circle is a set of points in a plane at a given distance from a given point in the plane. The given point is a center. CENTER.
Lesson 8-1: Circle Terminology
Chapter 10.1 Notes: Use Properties of Tangents Goal: You will use properties of a tangent to a circle.
Use Properties of Tangents
Chapter 10 Circles Section 10.1 Goal – To identify lines and segments related to circles To use properties of a tangent to a circle.
Parabola Formulas Parabolas (Type 2)Parabolas (Type 1) Vertex Form Vertex: (h, k) Axis: x = h Vertex: (h, k) Axis: y = k Rate: a (+ up / –down) Rate: a.
Unit 1 – Conic Sections Section 1.2 – The Circle Calculator Required.
Algebra 2 Conic Sections: Circles and Parabolas. Circles I can learn the relationship between the center and radius of a circle and the equation of a.
Making graphs and solving equations of circles.
Circles in the Coordinate Plane I can identify and understand equations for circles.
Section 9-3 Circles Objectives I can write equations of circles I can graph circles with certain properties I can Complete the Square to get into Standard.
Standard Form of a Circle Center is at (h, k) r is the radius of the circle.
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)
9-5 Tangents Objectives: To recognize tangents and use properties of tangents.
Equations of Circles. Vocab Review: Circle The set of all points a fixed distance r from a point (h, k), where r is the radius of the circle and the point.
1.1 and 1.5 Rectangular Coordinates and Circles Every man dies, not every man really lives. -William Wallace.
Chapter 14: CIRCLES!!! Proof Geometry.
 No talking!  No textbooks  Open notes/HW/worksheets  No sharing with your classmates  20 minute time limit.
1.1 and 1.5 Rectangular Coordinates and Circles Every man dies, not every man really lives. -William Wallace.
9.6 Circles in the Coordinate Plane Date: ____________.
8.1 The Rectangular Coordinate System and Circles Part 2: Circles.
Graphing Circles and Writing Equations of Circles.
Equation of Circle Midpoint and Endpoint Distance Slope
Section 2.8 Distance and Midpoint Formulas; Circles.
Holt Geometry 11-7 Circles in the Coordinate Plane 11-7 Circles in the Coordinate Plane Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation.
Circle Equations. Definitions Circle: The set of all points that are the same distance from the center Radius: a segment whose endpoints are the center.
Advanced Algebra H Notes Section 9.3 – Graph and Write Equations of Circles Objective: Be able to graph and write equations of circles. A _________ is.
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)
10-8 Equations of Circles 1.Write the equation of a circle. 2.Graph a circle on the coordinate plane.
Standard Form of a Circle Center is at (h, k) r is the radius of the circle.
CIRCLES Topic 7.3.
11.0 Analytic Geometry & Circles
Section 10.1 – The Circle.
COORDINATE PLANE FORMULAS:
CIRCLES Topic 10.2.
Circles 4.1 (Chapter 10). Circles 4.1 (Chapter 10)
Circles Tools we need for circle problems:
9.3 Graph and Write Equations of Circles
Circles in the Coordinate Plane
Tangents to Circles.
LT 11.8: Write equations and graph circles in the coordinate plane.
Find the center and radius of a circle with equation:
Warmup Find the distance between the point (x, y) and the point (h, k).
CIRCLES Topic 7.3.
CIRCLES Topic 7.3.
CIRCLES Topic 7.3.
Presentation transcript:

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 PLANE FORMULAS :

CIRCLE: The set of all points that are equidistant from a given point. GIVEN POINT:CENTER EQUIDISTANT: RADIUS (x 1, y 1 ) (x 2, y 2 ) (x 3, y 3 ) d1d1 d2d2 d3d3 (x, y) Distance #1: (x 1, y 1 ) Distance #2 : (x 2, y 2 ) Distance #3: (x 3, y 3 ) If all 3 points are on the circle, then all distances are equal!! d 1 = d 2 = d 3

CIRCLE FORMULA: Standard Form Center: (h, k) Radius: r (x, y) (h, k) Derive Formula: Distance

1.IDENTIFY the center and radius in the equation. a. Center: _________Radius: ________ b. Center: _________Radius: ________ c. Center: _________Radius: ________ PRACTICE #1: Interpret Equation of a Circle (2, -5) (4, 7) (-1, -3)

2. Write an equation of the circle with a center (-1, 3) and radius of 6. PRACTICE #2: Write the Equation of a Circle 3. Write the equation of the circle pictured to the right

4. (-1, 7) and (5, -1) PRACTICE #3: Write the equation of the circle given the endpoints of a diameter. 5. (-3, 4) and (-7, -6) Center:(2, 3) Center:(-5, -1)

6. (-3, -5) and (6, 2) PRACTICE #3 : Continued 7. (4, 8) and (4, -2) Center:(4, 3) Center:(1.5, -1.5)

HOW TO: Writing Circles in standard form Center: (-4, 6) Radius: 9 Step #1: Group x and y terms separately together Step #2: Move the constant term to the opposite side Step #3: Complete the square for x’s and y’s (Add Both to Right Side) Step #1: Step #2: Step #3:

PRACTICE #4: Writing Circles in Standard Form [A] Write in standard form, find the radius and center. Sketch a graph [B] Center: (3, 0) Radius: r = 4 Center: (2, -4) Radius:

PRACTICE #4: Continued [C] Write in standard form, find the radius and center. Sketch a Graph. [D] Center: ( -3/2, 0) Radius: r = 2 Center: (3, -5) Radius:

[E] Center: (-3, -4) Radius: r = 4 PRACTICE #4: Continued Write in standard form, find the radius and center. [F] Center: (5, -8) Radius: r = 5

PRACTICE #5: Equations given the a Tangent [A] Center: (-4, -3) Tangent to x-axis Write the equation of the circle given its tangency to an axis. [B] Center: (3, 5) tangent to y-axis TANGENT : A line intersecting at exactly one point with another curve. Additional Fact: Tangents are perpendicular to the curve.