SOLUTION: Identify the conic section represented by each equation. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyberbola, gi

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Identify the conic section represented by each equation. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyberbola, gi      Log On


   

Question 79487This question is from textbook Algebra 2
: Identify the conic section represented by each equation. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyberbola, give the center and foci. Sketch the graph.
3y%5E2-x-6y%2B5=0 This question is from textbook Algebra 2

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Identify the conic section represented by each equation. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyberbola, give the center and foci. Sketch the graph.
3y%5E2-x-6y%2B5=0
It is a parabola because it only has ONE squared letter.
Get all the terms in the squared letter on the left and
all other terms on the right:
3y%5E2-6y=x-5
Factor out the coefficient of y%5E2 on the left:
3%28y%5E2-2y%29+=+x-5
Complete the square by adding 1 inside the parentheses
on the left. However note that when we placing a 1
inside the parentheses on the left, we are really adding 3
because of the 3 multiplier in front of the parentheses
so we must add 3 to the right side to offset.
3%28y%5E2-2y%2B1%29+=+x-5%2B3
Factor the trinomial on the left side as a perfect square,
and combine terms on the right:
3%28y-1%29%5E2+=+x-2
Multiply both sides by 1%2F3
%281%2F3%293%28y-1%29%5E2+=+%281%2F3%29%28x-2%29
1%28y-1%29%5E2+=+%281%2F3%29%28x-2%29
%28y-1%29%5E2+=+%281%2F3%29%28x-2%29
Now the equation is in the form:
%28y-k%29%5E2+=+4p%28x-h%29
where the vertex is (h,k) = (2,1)