Question

The graph of an ellipse is shown.

Which equation represents this ellipse?

A. x²/10 + y²/4 = 1

B. y²/10 + x²/4 = 1

C. x²/25 + y²/4 = 1

D. y²/25 + x²/4 = 1

Answer 1

Answer:

D. y²/25 + x²/4 = 1

Step-by-step explanation:

Ellipse has a general equation of $\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} }=1$

We can see that the ellipse is stretched to 5 space in the y-axis. So our b-value is 5 giving us:

$\frac{y^{2} }{b^{2}}=\frac{y^{2} }{5^{2}}=\frac{y^{2} }{25}$

Then we also see that the ellipse is stretched 2 space in the x-axis, so our a-value is 2 giving us:

$\frac{x^{2} }{a^{2}}=\frac{x^{2} }{2^{2} }=\frac{x^{2} }{4}$

put the two together and we get

$\frac{x^{2} }{4}+\frac{y^{2} }{25}=1$

Answer 2

The answer is  y²/25 + x²/4 = 1 option D

The General form of the ellipse:

The standard equation for an ellipse, x² / a²+ y²/ b² = 1, represents an ellipse centered at the origin and with axes lying along the coordinate axes.

Which equation represents this ellipse?

A. x²/10 + y²/4 = 1

B. y²/10 + x²/4 = 1

C. x²/25 + y²/4 = 1

D. y²/25 + x²/4 = 1

According to the standard equation of the ellipse:

See in the given figure,
We can see that the ellipse is stretched to 5 spaces on the y-axis. So our b-value is 5 giving us: y²/b² = y²/5² = y²/25.

Then we also see that the ellipse is stretched 2 spaces on the x-axis, so our a-value is 2 giving us: x²/a² = x²/2² = x²/4

Put the two together and we get,

x²/4 + y²/25 = 1 is the required equation that represents the ellipse.

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