Answer:
Domain : x ∈ Real Numbers
Range : y ≥ 30
Step-by-step explanation:
The given equation is:
[tex]y^2-9x^2=900[/tex]
Simplifying it
[tex]\frac{y^2}{900}-\frac{9x^2}{900}=\frac{900}{900}\\\frac{y^2}{900}-\frac{x^2}{100}=1\\\frac{y^2}{30^2}-\frac{x^2}{10^2}=1[/tex]
Where Standard equation of parabola is:
[tex]\frac{y^2}{a^2}-\frac{x^2}{b^2}=1[/tex]
Which are similar. Conic Section is a parabola.
Find Domain and Range:
Simplify the given equation:
[tex]y^2-9x^2=900\\y=\sqrt{9x^2+900},y=-\sqrt{9x^2+900}\\y=3\sqrt{x^2+100},y=-3\sqrt{x^2+100}[/tex]
For whatever value of x, term under the square root always remains positive, so
Domain : x ∈ Real Numbers
For minimum value of x i.e 0, y=30. If we increase x, y also increases. So
Range : y ≥ 30
