Intro to Conic Section (Parabol, Ellipse)
- 2. Conic Section – a curve formed by the intersection of a plane and a double cone. By changing the plane, you can create a circle, ellipse, parabola or hyperbola
- 3. Identify as a circle, ellipse, parabola or hyperbola and explain why. •25x2 + 4y2 = 100 •x2 + y2 = 4 •2x2 – y2 = 16 •x2 – y = 12 •5x2 + 6x – 4y = x2 – y2 – 2x •3x2 – 2y2 + 32y – 134 = 0 •7x2 – 28x + 4y2 + 8y = -4 •2x2 + 12x + 18 – y2 = 3(2 – y2 ) + 4y •2x2 + 3x – 4y + 2 = 0 ellipse circle hyperbola parabola ellipse hyperbola ellipse circle parabola
- 4. 10.3 Circles A circle is the set of all points in a plane that are a distance r (radius) from a given point called the center.
- 5. x2 + y2 = r2 center (0,0) radius = r Standard Form: (x – h)2 + (y – k)2 = r2 Center (h, k) Radius = r
- 6. Ex 1 •Write in standard form and graph. •Radius = 3, center (3, -2) 2 2 3 2 9 x y
- 7. Ex 2 •Translate the circle down 1 unit and right 2 units: (x – 2)2 + (y + 1)2 = 16 2 2 4 2 16 x y
- 8. Ex 3 •Find the center and radius: (x + 4)2 + (y – 2)2 = 36 : 4,2 C 6 r
- 9. Ex 4 •Write the equation of the circle that has diameter from (5, 4) to (-2, -6) 2 2 2 1 2 1 ( ) ( ) d x x y y 2 2 ( 2 5) ( 6 4) d 2 2 ( 7) ( 10) d 149 d 149 2 r 2 1 2 1 , 2 2 x x y y 2 5 6 4 , 2 2 3 , 1 2 2 2 3 149 1 2 4 x y
- 10. Ex 5 •A line that intersects a circle in exactly one point is said to be tangent to the circle. •Write the equation of the circle that has center (-4, -3) and is tangent to the x-axis. 2 2 4 3 9 x y
- 11. Ex 6 •Write in standard form. Find c and r. x2 + y2 – 4x + 8y – 5 = 0 2 2 5 4 8 y x x y 2 2 8 4 4 4 6 16 5 1 x y x y 2 2 5 2 2 4 y x :(2, 4) 5 C r
- 12. Ex 7 •Write in standard form. Find c and r. x2 + y2 + 6x – 7 = 0 2 2 7 6 x x y 2 2 6 9 9 7 x x y 2 2 6 3 1 0 y x :( 3,0) 4 C r
- 13. WS 10.0 Circles