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Circles HW #1

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**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!

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**Solve by completing the square:**

x2 + 6x – 16 = 0 x2 – 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**

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 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

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**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 < 102 ? Substitute for x and y. 97 < 100 The inequality is true. ANSWER So, you are in the tower’s range.

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HOMEWORK Circle Homework #2 WS

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