PreCalculu

Notes

PreCalculus ENGR. OSCAR H. HALAMANI, JR. Conic Sections  General Form of Equation of a Circle  Standard Form <=> General Form  Determining the parts of the circle given its General Form of Equation  Situational problems involving Circle At the end of the lesson, the student is able to: 1. Familiarize the General Form of Equation of a Circle 2. Convert the Standard form of Equation of a circle to its General Form and vice versa 3. Determine the parts of a circle given is its General Form of Equation 4. Solve situational problems involving circle @ C ( 0, 0) : @ C ( h, k) : x2 + y2 = r2 (x - h)2 + (y - k)2 = r2 Ax2 + Cy2 + Dx + Ey + F = 0 where: A = C Ex. (x - 2)2 + (y + 3)2 = 25 (a ± b)2 = a2 ± 2ab + b2 x2 - 4x + 4 + y2 + 6y + 9 = 25 x2 + y2 - 4x + 6y + 4 + 9 - 25 = 0 x2 + y2 - 4x + 6y - 12 = 0 1. Determine the C(h,k) and r of the following a. x2 + y2 - 1 = 0 36 36 x2 + y2 - 36 = 0 x2 + y2 = 36 Ans. C (0,0) r = √36 = 6 b. x2 + y2 + 10x - 24 = 0 x2 + 10x + y2 = 24 x2 + 10x + 25 + y2 = 24 + 25 (x + 5)2 + y2 = 49 Ans. C (-5,0) r = √49 = 7 c. x2 + y2 + 6x - 2y + 1 = 0 x2 + 6x + + y2 - 2y = - 1 x2 + 6x + 9 + y2 - 2y + 1 = - 1 + 9 + 1 (x + 3)2 + (y - 1)2 = 9 C ( - 3, 1) r = 3 Ans. d. ...