Fill in the blanks Suppose we want to graph an equation in x

Fill in the blanks. Suppose we want to graph an equation in x and y. If we replace X by X - 3, the graph of the equation is shifted to the by 3 units. If we replace X by X + 3 the graph of the equation is shifted to the by 3 units. If we replace V by V - 1 , the graph of the equation is shifted by 1 unit. If we replace V by V + 1 , the graph of the equation is shifted by 1 unit. The polar equations r = ed/1 plusminus ecos(theta) and r = ed/1 plusminus esin(theta) represent conics. The conic is a parabola if an ellipse if a hyperbola if

Solution

1

a) if x is replced by x-3 then the graph is shifted by 3 units to right.

if x is replced by x+3 then the graph is shifted by 3 units to left.

b) if y is replaced by y-1 then the graph of equation is shifted verically down by 1 unit.

if y is replaced by y+1 then the graph of equation is shifted verically up by 1 unit.

2) The conic is

a parabola if the eccentricity equals 1,which means e=1

a ellipse if the eccentricity greater than 0 and less than 1,which means 0<e<1

a hyperbola if the eccentricity is greater 1,which means e >1