Presentation on theme: "EXAMPLE 1 Graph an equation of a circle"— Presentation transcript:
1 EXAMPLE 1Graph an equation of a circleGraph y2 = – x Identify the radius of the circle.SOLUTIONSTEP 1Rewrite the equation y2 = – x in standard form as x2 + y2 = 36.STEP 2Identify the center and radius. From the equation, the graph is a circle centered at the origin with radiusr = = 6.
2 EXAMPLE 1Graph an equation of a circleSTEP 3Draw the circle. First plot several convenient points that are 6 units from the origin, such as (0, 6), (6, 0), (0, –6), and (–6, 0). Then draw the circle that passes through the points.
3 Write an equation of a circle EXAMPLE 2Write an equation of a circleThe point (2, –5) lies on a circle whose center is the origin. Write the standard form of the equation of the circle.SOLUTIONBecause the point (2, –5) lies on the circle, the circle’s radius r must be the distance between the center (0, 0) and (2, –5). Use the distance formula.r = (2 – 0)2 + (–5 – 0)2==The radius is29
4 Write an equation of a circle EXAMPLE 2Write an equation of a circleUse the standard form with r to write an equation of the circle.=x2 + y2 = r2Standard form= ( )2x2 + y2Substitute for r29x2 + y2 = 29Simplify
5 EXAMPLE 3Standardized Test PracticeSOLUTIONA line tangent to a circle is perpendicular to the radius at the point of tangency. Because the radius to the point(1–3, 2) has slope=2 – 0– 3 – 0=23–m
6 Standardized Test Practice EXAMPLE 3Standardized Test Practicethe slope of the tangent line at (–3, 2) is the negative reciprocal of or An equation of232–3the tangent line is as follows:y – 2 = (x – (– 3))32Point-slope form32y – 2 = x +9Distributive property3213y =x +Solve for y.ANSWERThe correct answer is C.
7 GUIDED PRACTICEfor Examples 1, 2, and 3Graph the equation. Identify the radius of the circle.1.x2 + y2 = 9SOLUTION3
10 GUIDED PRACTICEfor Examples 1, 2, and 34. Write the standard form of the equation of the circle that passes through (5, –1) and whose center is the origin.SOLUTIONx2 + y2 = 265. Write an equation of the line tangent to the circle x2 + y2 = 37 at (6, 1).SOLUTIONy = –6x + 37