University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2020
Views:

476

Pages:

8
Author:

larbiwxcvbn

Circles in the Coordinate Plane Objective: 1 • Derive the equation of а circle in both standard and general form • Graph а Circle • Use transformations • Find the radius and center from а given circle How do you draw а circle? What information do you need? 2 EQUATION OF А CПlCLE о Staпdard Forш: о r is the radius of the circle Things to reшember about staпdard forш equatioпs: • • • • А- sign means that h or k is а positive number А+ sign means that h or k is а negative number х2 or у2 (no parentheses) means that h and/or k is О То find the value of r, take the square root of r2 3 CL01D) QAD\.O� -== �(-о Fiпd the center апd radius of the circle from the equation given: (х - 2) 2 + (у - 3) 2 = 16 (х + 3) 2 + (у - 1) 2 = .,_ ·· - · ···-------- - (х + 5) 2 + (у - 7) 2 = 64 18 f2AD t l7 s ::: lp 4 1 EXAMPLE 1 0 Find the equation of thc _circlc whcn given the centc1· point and the rad1us Ccnter: (7,4) Ceпter: (5,2) 7 FINDING ТНЕ RADIUS FROM 2 POINTS о Use the formula for finding the length of а radius when given 2 points. It comes from taking the square root of both sides of а standard forn1 equation. о Remember that h and k соте f1·ош the ce11te1· pont and х and у will соте fl'oш tЬе otl1e1· giveп po1nt 1 ЕХАМРLЕ о Fiпd the staпdard equatioп of а circle wheп giveп GRAPHING CIRCLES center point and =-ra=-==-==--=-= о You пееd to kпow before you can gra о Follow these 3 Steps: • Graph the center point • Count up, down, left, and right (START ЕАСН COUNT FROM ТНЕ CENTER POINT) нsing the value of the radius to graph 4 more points • Connect the 4 outer points using smooth cнrved lines t ЕХАМРLЕ о Graph the following circle: (х - 2) 2 + (у - 1) 2 10 FINDING ТНЕ EQUATION OF А CIRCLE FROM ТНЕ GRAPH о We can find the standard form equation of а circle from а graph Ьу: • Find the location of the ceпter poiпt • Find the value of the radius Ьу counting from the center point out to the edge of the circle (up, down, left, or right) • Plug that information into the standard form equation of а circle 11 ЕХАМРLЕ о Find the standar:d form equation of the circle below: The general form of an equation of а circle is Ах 2 + Ву2 + Сх + Dy + Е == О, where А== В, А -f:. О, апd В-::/- О. This doesn't look as simple as the standaгd foгm. In fact, \Ve can't even gгaph from this form. Find the ce11ter апd xadius of the cu·cle described Ьу tl1e eqнation Find the center and xadius of the circle described Ьу the eqнation