What are the vertex, focus, and directrix of the parabola described by #(x − 5)^2 = −4(y + 2)#?
1 Answer
Aug 7, 2018
Explanation:
#"the standard form of a vertically opening parabola is"#
#•color(white)(x)(x-h)^2=4a(y-k)#
#"where "(h,k)" are the coordinates of the vertex and a"#
#"is the distance from the vertex to the focus and"#
#"directrix"#
#(x-5)^2=-4(y+2)" is in this form"#
#"with vertex "=(5,-2)#
#" and "4a=-4rArra=-1#
#"Focus "=(h,a+k)=(5,-1-2)=(5,-3)#
#"directrix is "y=-a+k=1-2=-1#
graph{(x-5)^2=-4(y+2) [-10, 10, -5, 5]}
