conic_sections_and_circles.pptxpptppptppppppt

conic

1. Precalculus: CONIC SECTIONS: CIRCLES

2. Session Objectives For this two -hour period, SHS students in Precalculus are expected to develop the following learning competencies: illustrate the different types of conic sections: parabola, ellipse, circle, hyperbola, and degenerate cases; define a circle; determine the standard form and general form of the equation of a circle; and graph a circle in a rectangular coordinate system.

3. Conic Sections Intersections of cones and planes 1

4. Starting with Basics Explain the following mathematical terms: Undefined Terms in Geometry Intersecting lines Parallel lines Perpendicular lines Angle Cone

5. What are CONIC SECTIONS ? If a plane intersects a double right circular cones, the intersection is a two-dimensional curve of different types. These curves are called conic sections . Also called conics, these different types are: CIRCLE ELLIPSE PARABOLA HYPERBOLA

6. What are CONIC SECTIONS ? CIRCLE ELLIPSE PARABOLA HYPERBOLA

7. DEGENERATE CASES

8. CIRCLES A circle is the set of all points equidistant to a fixed point. radius center

9. EQUATION OF A CIRLE Consider a circle plotted on the Cartesian Coordinate plane. Determine the coordinates of the center and its radius.

10. EQUATION OF A CIRLE Assume that we do not know the actual coordinates of the center. What if the center is at the point of origin?    

11. STANDARD FORM of the equation of a circle The standard form of the equation of a circle whose center is at the origin with radius, r , is For any circle whose center have coordinates (h, k) with radius, r , the standard form of its equation is  

12. STANDARD FORM of the equation of a circle Give the standard form of the equation of the circle described in each item below. Center at the origin, and r = and r = 10  

13. EQUATION OF A CIRLE Solve for the equation of the following circles: circle A circle B center (7,−2), r= 8 center (-8,0 ) r= 11

14. C h eck your Understanding Find the center and radius of the given circle. + =100 + = + =16 = 10 =121  

15. GENERAL FORM of the equation of a circle The general form of the equation of a circle is w here  

16. GENERAL FORM of the equation of a circle Transform the following equations into the general form:  

17. Transforming equations Transform the following equations into the standard form:  

18. Transforming equations   Group the terms based on the variables. Complete the square to make each group of terms a perfect square trinomial (PST). Add the constants of the PSTs to the right side. Express the PSTs as squares of binomials