Writing equations for Circles

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Presentation transcript:

Writing equations for Circles

What are the 2 things you need to write an equation for a circle?? The Center: ( , ) The radius: r =

Write the equation of a circle with the given radius and whose center is the origin.

Writing equations: Example 5 Write the equation of the circle with the point (4,5) on the circle and the origin as it’s center.

Point (4,5) on the circle and the origin as it’s center. *Always look for Center: _______ and Radius: _____

Practice!! Write the equation of the circle with the point (-3,-5) on the circle and the origin as it’s center. *Always look for Center: _______ and Radius: _____

Standard Equation of a Translated Circle The standard equation for a circle with its center at (h, k) and a radius of r is: This is different with both h and k. Both of the numbers are the opposite when plugged in. Example: Write the standard equation for the translated circle with center at (-2, 3)and a radius of 4.

Practice!! Write the equation of the circle with the center (3,-1) and the radius . *Always look for Center: _______ and Radius: _____

Writing equations of circles Find equation of circle passing through (2, 5) with the center at (0,0) Find equation of circle passing through (-5, -5) with the center at (0,0) Find equation of circle passing through (5, 1) with the center at (2,-3) *Always look for Center: _______ and Radius: _____

You Try!! (Try a picture to help!) Find equation of circle passing through (-3, 4) with the center at (0,0) Find equation of circle passing through (0,2) with the center at (-6,3) Find equation of circle passing through (-2, -2) with the center at (-5,-8) *Always look for Center: _______ and Radius: _____

Find an equation of a line tangent to a circle Last thing!! Find an equation of a line tangent to a circle Find an equation of a line tangent to the circle at (-1, 3) The tangent line is perpendicular to the line from the origin to the point. You’ll have slope and a point. Write the equation.

You Try!! Find an equation of a line tangent to the circle at (4, -1) Find the slope from the center to the point (rise over run) Find the Perpendicular slope (opposite reciprocal) Write an equation with your NEW slope and point given y = mx+b or y – y1 = m(x – x1)

Practice WS Front and Back! Circle Practice!! Practice WS Front and Back!