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Circles HW #1

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Complete the square and write as a squared binomial. 1.1.x 2 + 6x + _____ = _____________ 2.2.x 2 – 10x + _____ = _____________ 3.3.x x + _____ = _____________ 4.4.x 2 + 2x + _____ = _____________ 5.5.x 2 – 5x + _____ = ______________6. This will be a critical skill we will use later on with conic sections!

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Solve by completing the square: x 2 + 6x – 16 = 0 x 2 – 4x = 11

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Write the equation in standard form for the given circle:

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

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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

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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

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

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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.

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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….

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

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

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

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

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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)

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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 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: x 2 + y 2 < 10 2 In the diagram above, the origin represents the tower and the positive y -axis represents north.

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Write a circular model continued…. STEP 2 Substitute the coordinates (4, 9) into the inequality from Step 1. x 2 + y 2 < 10 2 Inequality from Step < 10 2 ? Substitute for x and y. The inequality is true. 97 < 100 ANSWER So, you are in the tower’s range.

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HOMEWORK Circle Homework #2 WS

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