Question

Is the ellipse represented by the equation (x-5)^2/3 (x 1)^2/5?

Answer 1

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Answer 2

Answer:

Yes, It is ellipse

Step-by-step explanation:

Given Equation : $\dfrac{(x-5)^2}{3}+\dfrac{(y+1)^2}{5}=1$

The standard equation of ellipse

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

If we compare the given equation with standard equation of ellipse. It would be same.

Yes, the given equation represents ellipse.

The center of ellipse (5,-1)

$a=\sqrt3$

$b=\sqrt5$

• If a>b then horizontal ellipse.

• If a<b then vertical ellipse.

For the given equation $\sqrt3<\sqrt5\Rightarrow a<b$

Therefore, it is vertical ellipse.

Graph: Please find attachment