Circle Equations Lecture Notes PDF
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De La Salle
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Summary
These lecture notes provide an overview of circles, including their standard and general equations, along with applications and graph analysis. The notes cover various aspects and example problems related to circles in mathematics.
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PRECAL 1 Circle The Standard and General Form of an equation with center at origin and with center at C(h, k) Conditions to determine an equation of a circle Applications: Problems involving circles Circle and their Equations A circle is the locus of a poin...
PRECAL 1 Circle The Standard and General Form of an equation with center at origin and with center at C(h, k) Conditions to determine an equation of a circle Applications: Problems involving circles Circle and their Equations A circle is the locus of a point that moves in a plane so that its distance from a fixed point remains constant. Radius is the constant distance (segment connecting the center and any point on the circle). Center is the fixed point (not on the curve of a circle) equidistant from any point on the circle. Chord is the segment connecting any two points of a circle. Diameter is the longest chord of a circle, that is, one connecting any two points of a circle and passing through the center. Tangent line is a line that touches the circle at exactly one point called the point of tangency. Standard Forms of Equation The following are equations of circles each in standard form. General Equation of a Circle Nature of the Graph a. If , there is a graph and it is a circle b. If , the graph is a single point sometimes called a POINT CIRCLE (but not a circle) a. If , there is no graph since r is imaginary Reduce the equation of to the standard form of a circle. Identify the radius, center and draw the graph. Reduce the equation of to the standard form of a circle. Identify the radius, center and draw the graph. Reduce the equation of to the standard form of a circle. Identify the radius, center and draw the graph. Reduce the equation of to the standard form of a circle. Identify the radius, center and draw the graph. Reduce the equation of to the standard form of a circle. Identify the radius, center and draw the graph. Activity Reduce the equation of the circle to its standard form. Identify the center and radius and graph if possible. 4x^2 + 4y^2 +4x - 20y-8 = 0 ACTIVITY 1. Identify the center, radius, graph (if possible), circumference and area of a circle whose equation is 2. An equilateral triangle is inscribed in a circle whose equation is. Determine the area of each segment of the circle formed. Also, find the area of the equilateral triangle. 3. Find the general equation of the circle passing through the points M(-1,-4), A(3,-2) and U(5,2).
