Question

What is the center of the ellipse x2+5y2–45=0?

Answer 1

Answer:

Center is at (0,0)

Step-by-step explanation:

An equation of ellipse in standard form is:

$\displaystyle{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2} = 1$

Where center is at point (h,k)

From the equation of $\displaystyle{x^2+5y^2-45=0}$. First, we add 45 both sides:

$\displaystyle{x^2+5y^2-45+45=0+45}\\\\\displaystyle{x^2+5y^2=45}$

Convert into the standard form with RHS (Right-Hand Side) equal to 1 by dividing both sides by 45:

$\displaystyle{\dfrac{x^2}{45}+\dfrac{5y^2}{45}=\dfrac{45}{45}}\\\\\displaystyle{\dfrac{x^2}{45}+\dfrac{y^2}{9}=1}$

Therefore, the center of ellipse is at (0,0) since there are no values of h and k.