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Distance and Midipoint Formula; Circle
Objectives:
1. To find the distance between two points
2. To find the midpoint of a line segment
3. To write the standard form of a circle’s equation
4. To give the center and radius of a circle whose
equation is in standard form
5. To convert the general form of a circle’s equation to
standard form
Objective 1: To find the distance between two points
The distance Formula
Given two points P_{1}(x_{1},y_{1}) and P_{2}(x_{2},y_{2})
Example: Find the distance between (4, 1) and (2,  3).
Objective 2: To find the midpoint of a line segment
Finding the midpoint
Formula :
Find the midpoint of the line segment with endpoints
(4,1) and (2,  3)
Objective 3: To write the standard form of a circle’s
equation
Circle:
A circle is the set of all points in a plane that are
equidistant from a fixed point called the center. The fixed
distance from the circle’s center is called the radius.
Find the formula of a circle whose center is (h, k) and
radius is r.
The equation of a circle whose center is at the origin and
radius r is x^{2} + y^{2} = r^{2}.
Write the standard form of the equation of the circle with
center at (0,0) and the radius is 4. Graph the circle on the
board.
Equation: x^{2} + y^{2} = 16.
Write the standard form of the equation of a circle with
center (2, 1) and radius 2. Graph circle on the board.
Equation:
Objective 4: To give the center and radius of a circle
whose equation is in standard form
Give the center and radius of a circle whose equation is
(x + 4)^{2} + (y + 5)^{2} = 36.
The center is (4,5) and the radius is 6.
Objective 5:
To convert the general form of a circle’s equation to
standard form
The general form of the equation of a circle is
x^{2} + y^{2} Dx + Ey + F= 0
Standard Form: (x  h)^{2} + (y – k)^{2} = r^{2}
Express x^{2} + y^{2} +8x + 4y + 16= 0 in standard form and
find the center and the radius.
Center: (4,2) and radius = 2
Express x^{2} + y^{2}  6y  7= 0 in standard form and find the
center and the radius.
Center: (0, 3) and radius is 4
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