Question 967997
For the following equation of a parabola determine the vertex, focus, and directrix:
y2+2x−8y+7=1
y^2-8y+2x=-6
complete the square:
(y^2-8y+16)-16+2x=-6
(y-4)^2=-2x+10
(y-4)^2=-2(x-5)
This is an equation of a parabola that opens leftward
Its basic form of equation: (y-k)^2=4p(x-h), (h,k)=coordinates of vertex
For given parabola:
vertex: (5, 4)
axis of symmetry: y=4
4p=2
p=1/2
focus:(4.5,4) (p-distance left of vertex on the axis of symmetry)
directrix: x=5.5 (p-distance right of vertex on the axis of symmetry)