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. 25x 2 + 4y 2 = 100 x 2 + y 2 = 4 2x 2 – y 2 = 16 x 2 – y = 12 5x 2 + 6x – 4y = x 2 – y 2 – 2x 3x 2 – 2y y – 134 = 0 7x 2 – 28x + 4y 2 + 8y = -4 2x x + 18 – y 2 = 3(2 – y 2 ) + 4y 2x 2 + 3x – 4y + 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 – 4x + 8y – 5 = 0

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

WS 10.0 Circles