Math All Conics

Center: (-4, 6) Radius: 4 Given the center and radius, write the equation.

(x + 4)² + (y - 6)² = 16

Center: (2, 4) Passes through: (1, 2) Find the equation of the circle.

(x - 2)² + (y - 4)² = 5

Center: (5, -4) Tangent to the y-axis. Find the equation of the circle.

(x - 5)² + (x + 4)² = 25

Endpoints of the diameter: (2, 5) and (-2, -2) Find the equation of the circle.

(x)² + (y - 2)² = 13

What is the general formula for a circle?

1(x - h)² + 1(y-k)² = r²

Equation x² + y² +2x - 4y - 3 = 0 Graph.

Center: (-1, 2) Radius: √8

7x² + 7y² = 441 State the center and radius.

Center: (0, 0) Radius: √63

Equation: (x - 2)² + (y + 1)² = 17 Graph.

Center: (2, -1) Radius: √17

(x - 2)² + (y + 3)² = 25 State the center and give the radius. Graph.

Center: (2, -3) Radius: 5

x² + y² - 6x + 4y = 12 Write the equation in standard form. State the center and give the radius. Graph.

Standard form: (x - 3)² + (y+2)² = 25 Center: (3, -2) Radius: 5

x²/16 + y²/64 = 1 Identify the major axis vertices, minor axis vertices, center, and foci. Graph.

a = 8 b = 4 c = 4√3 Vertices: (0, 8) and (0, -8) Co-vertices: (4, 0) and (-4, 0) Foci: (0, 4√3) and (0, -4√3)

(ellipse) What does the h, k, a, and b stand for in the formula? What are the foci?

h = x-value of the center k = y-value of the center So, center = (h,k) a = distance along major axis (it is the bigger number) b = distance along minor axis Foci = distance from center along major axis

(circle) What does the h, k, and r stand for in the formula?

h = x-value of the center k = y-value of the center So, center = (h,k) r = radius

(ellipse) What equation do you use to find the c-value?

major axis² - minor axis² = foci² a² - b² = c²