10 0 Conic Sections Conic Section a curve

10. 0 Conic Sections

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

Identify as a circle, ellipse, parabola or hyperbola and explain why. • 25 x 2 + 4 y 2 = 100 • x 2 + y 2 = 4 • 2 x 2 – y 2 = 16 • x 2 – y = 12 • 5 x 2 + 6 x – 4 y = x 2 – y 2 – 2 x • 3 x 2 – 2 y 2 + 32 y – 134 = 0 • 7 x 2 – 28 x + 4 y 2 + 8 y = -4 • 2 x 2 + 12 x + 18 – y 2 = 3(2 – y 2) + 4 y • 2 x 2 + 3 x – 4 y + 2 = 0

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.

x 2 + y 2 = r 2 center (0, 0) radius = r Standard Form: (x – h)2 + (y – k)2 = r 2 Center (h, k) Radius = r

Ex 1 • Write in standard form and graph. • Radius = 3, center (3, -2)

Ex 2 • Translate the circle down 1 unit and right 2 units: (x – 2)2 + (y + 1)2 = 16

Ex 3 • Find the center and radius: (x + 4)2 + (y – 2)2 = 36

Ex 4 • Write the equation of the circle that has diameter from (5, 4) to (-2, -6)

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.

Ex 6 • Write in standard form. Find c and r. x 2 + y 2 – 4 x + 8 y – 5 = 0

Ex 7 • Write in standard form. Find c and r. x 2 + y 2 + 6 x – 7 = 0

WS 10. 0 Circles