SOLUTION: I have to determine if this is a circle (and find the radius and center) a parabola (find the vertex focus and directrix) or if is an ellipse or hiperbola find the foci and sketch
Algebra ->
Quadratic-relations-and-conic-sections
-> SOLUTION: I have to determine if this is a circle (and find the radius and center) a parabola (find the vertex focus and directrix) or if is an ellipse or hiperbola find the foci and sketch
Log On
Question 815515: I have to determine if this is a circle (and find the radius and center) a parabola (find the vertex focus and directrix) or if is an ellipse or hiperbola find the foci and sketch it. My problem to solve is y^-2y+16x-31= 0 Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! I have to determine if this is a circle (and find the radius and center) a parabola (find the vertex focus and directrix) or if is an ellipse or hiperbola find the foci and sketch it. My problem to solve is
y^2-2y+16x-31= 0
complete the square:
(y^2-2y+1)+16x=31+1
(y-1)^2+16x=32
(y-1)^2=-16x+32
(y-1)^2=-16(x-2)
This is an equation of a parabola that opens leftwards.
Its basic form of equation: (y-k)^2=-4p(x-h), (h,k)=(x,y) coordinates of the vertex.
For given parabola:
vertex:((2,1)
axis of symmetry: y=1
4p=16
p=4
Focus:(-4,1) (p-distance to the left of the vertex on the axis of symmetry)
directrix:x=6 (p-distance to the right of the vertex on the axis of symmetry)
see graph below:
y=±(-16x+32)^.5+2
(