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Information about Analytical geometry

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HISTORY Introduced in the 1630s Aided the development of calculus RENE DESCARTES (1596-1650) and PIERRE DE FERMAT (1601-1665), French mathematicians, independently developed the foundations for analytical geometry

CARTESIAN PLANE

• x-axis (horizontal axis) where the x values are plotted along. • y-axis (vertical axis) where the y values are plotted along. • origin, symbolized by 0, marks the value of 0 of both axes • coordinates are given in the form (x,y) and is used to represent different points on the plane.

Slope of a Line

Slope of a Line

Slope of a Line

Slope of a Line

Slope of a Line

Inclination of a Line y y L L θ O M x θ O M x

Angle between Two Lines

Angle between Two Lines • If θ is angle, measured counter-clockwise, between two lines, then • where m2 is the slope of the terminal side and m1 is the slope of the initial side

SLOPE OF PARALLEL LINES

SLOPE OF PERPENDICULAR LINES

Sample Problems

EQUATION OF A CIRCLE

EQUATION OF CIRCLE (origin is not the center) A (h, k) B ( x, y)

Graph the following circle.

REFERENCES - Demirdag, M. (2013). Analytic geometry [PowerPoint Presentation]. Available at: http://www.slideshare.net/mstfdemirdag/analytic-geometry-8693115. Accessed on: 4 March 2014 - Felipe, N, M. (2013). Analytic geometry basic concepts [PowerPoint Presentation]. Available at: http://www.slideshare.net/NancyFelipe1/analytic-geometry-basic-concepts.Accessed on: 4 March 2014 - Marasigan, D. (2013). Lecture #2 analytic geometry [PowerPoint Presentation]. Available at: http://www.slideshare.net/denmarmarasigan/lecture-2-analytic-geometry.Accessed on: 4 March 2014 - Marasigan, D. (2013). Lecture #3 analytic geometry [PowerPoint Presentation]. Available at: http://www.slideshare.net/denmarmarasigan/lecture-3-analytic-geometry.Accessed on: 4 March 2014 - Marasigan, D. (2013). Lecture #5 analytic geometry [PowerPoint Presentation]. Available at: http://www.slideshare.net/denmarmarasigan/lecture-5-analytic-geometry. Accessed on: 4 March 2014

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