LE HONG PHONG SPECIALIZED UPPER-SECONDARY SCHOOL- NAM DINH.

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Presentation transcript:

LE HONG PHONG SPECIALIZED UPPER-SECONDARY SCHOOL- NAM DINH

Three parts: 1. Some terms about circle and coordinate plane. 2.Equation of circle. 3.Some examples.

(C)Circle I CD R Line k AB Line AB 1.Pre-teaching new-terms Complete the following table

(C)Circle ICenter CDDiameter the largest distance between any two points on the circle. RRadius the length of a line segment joining the center to any point on the circle itself, which is half a diameter. Line kTangent a straight line that touches the circle at a single point. Segment AB Chord a line segment whose endpoints lie on the circle. Line ABSecant an extended chord, a straight line cutting the circle at two points AmBminor arcGiven two points on a circle, the minor arc is the shortest arc linking them. The major arc is the longest. 1.Pre-teaching new-terms

M(x;y) ( x;y ) : The coordinates of the point M x: The x-coordinate of M y: The y-coordinate of M

Solution 2.1 Problem 1. In the coordinate plane, given a point and a positive real number R. On what conditions that the point is on the circle Question:What is the formula to calculate the distance between two points? the distance from the point M to the point I is equal to R, that is (square both sides) (distance formula) The equation (1) is called the equation of the circle.,or M is on the circle if and only if

EXAMPLE 1 The equation of the circle is Solution Find the equation of the circle with centerand the radius

EXAMPLE 2 Solution Thus, the equation of the circle is Find the equation of the circle with center and passing through As the circle with center the radius of the circle is

EXAMPLE 3 Solution Given two points Find the equation of the circle with the diameter AB. and The center of the circle is the midpoint I of the line segment AB, then the coordinates of and the radius Hence, the equation of the circle with the diameter AB is What is the formula to calculate the coordinates of the midpoint of a line segment AB?

Hence, the equation of the circle (C) is EXAMPLE 4 Find the equation of the circle (C) centered at and tangent to the line d with the equation Solution The line d is tangent to the circle (C) iff or Let R be the radius of the circle (C). What is the formula to calculate the perpendicular distance from a given point to a given line?

Wrapping-up 1.Center I(a;b) Two quantities are needed to find the equation of the circle 2. Radius R Then use the formula

Homework