Question 459152: Determine whether x^2+y-81=0 is symmetric with respect to the x-axis, y-axis and or origin Found 2 solutions by math-vortex, robertb:Answer by math-vortex(648) (Show Source):
You can put this solution on YOUR website! We want to know which type of conic section this equation represents. Let's manipulate the equation with algebra to put it into standard form. Then it will be easy to see if it is a parabola, an ellipse, or a hyperbola.
Isolate the x-squared term on the left side of the equation.
This is the standard form of the equation of a parabola. In general, it looks like this: where (h,k) is the vertex of the parabola. Since the x-term is squared, we know that the parabola opens up if a>0 (positive) and opens down if a<0.
In your equation, the vertex of the parabola is (0,-81) which is on the y-axis. Since a=-1, the parabola opens down. Therefore, the parabola is symmetric with respect to the y-axis.
You can put this solution on YOUR website! Change (x,y) to (-x,-y): <==> , a different equation from the original. Hence no symmetry with respect to origin.
Change (x,y) to (x,-y): <==> , a different equation from the original. Hence no symmetry with respect to x-axis.
Change (x,y) to (-x,y): <==> , the same equation as the original. Hence there is symmetry with respect to the y-axis.
