Section 101 HWK httpswwwwel udentAssignment Responsessubmit

Section 10.1 HWK | https//www.wel udent/Assignment -Responses/submit?dep 13689025 Find the vertex, focus, and directrix of the paraboa and sketch its graph. Use a graphing utility to verify your graph. y2-12y-4x=-32 vertex (x, y) focus (x, y) = drectrb 1. Select an object from the Tools menu to the left 2 Enter coordinates in Object Properties below, or use the mouse to place and move objects. To enter a fractional or decimal coordinate, use Object Properties View our tutorial videos I\'m Cortana. Ask me anything

Solution

y^2 -12y -4x = -32

Reaaranging:

y^2 -12y +36 -36 = 4x -32

(y -6)^2 = 4x -32 +36

(y -6)^2 = 4(x+1)

Comparing with standard parabolic equation : 4p(x-h) =( y- k)^2

Vetex ( -1, 6)

p = 1

Parabola is symmetric around the x axis so focus lies a distance p from centre (-1, 6) along x axis

Focus ( -1 +p, 6) = ( 0 , 6)

directrix : x = -1 -p = -1 -1 = -2

x = -2