Sketch the Graph of x^2=y^2=9
x^2=y^2=9
x^2 - y^2=9
x^2 /9 - y^2 / 9 = 1
You have a hyperbola with centre (0,0) and a=3, and b=3
vertices are (3,0) and (-3,0)
draw a square with sides 6 and centre it at the origin
draw the diagonals of this square and extend them in all four directions.
These two extended diagonal are the asymptotes of your hyperbola
Sketch your two parts of the hyperbola with centres given above and approaching these asymptotes
Find the equation of a hyperbola which is generated by a point that moves so that the difference of its distance from the points (-4,1) and (2,1) is 4.
To sketch the graph of the equation x^2 = y^2 = 9, we first need to understand what this equation represents.
The equation x^2 = 9 implies that the square of the x-coordinate is equal to 9. Similarly, the equation y^2 = 9 implies that the square of the y-coordinate is equal to 9.
Since the square of a negative number and the square of its positive counterpart both result in the same positive value, we would have two branches for each equation. Let's examine each branch separately:
For the equation x^2 = 9, we have:
- If x = 3, then 3^2 = 9.
- If x = -3, then (-3)^2 = 9.
So, we have two x-values for the equation x^2 = 9, which are x = 3 and x = -3. These correspond to points along the x-axis.
Similarly, for the equation y^2 = 9, we have:
- If y = 3, then 3^2 = 9.
- If y = -3, then (-3)^2 = 9.
So, we have two y-values for the equation y^2 = 9, which are y = 3 and y = -3. These correspond to points along the y-axis.
To sketch the graph, we plot these points (3, 0), (-3, 0), (0, 3), and (0, -3). Connecting these points will give us the graph.
The graph will consist of a vertical line passing through (3, 0) and (-3, 0), as well as a horizontal line passing through (0, 3) and (0, -3). These two lines intersect at the origin, (0, 0).
The graph of x^2 = y^2 = 9 is a plus-shaped figure, resembling an “X” shape, with the origin serving as its center point.