Question

Which of the following is the domain and range of the ellipse with equation x2 + 4y2 – 2x + 16y – 19 = 0?

D: [–1, 5]; R: [–7, 5]
D: [–5, 7]; R: [–5, 1]
D: [–5, 1]; R: [–5, 7]
D: [–7, 5]; R: [–1, 5]

Answer 1

The option second D: [–5, 7]; R: [–5, 1] is correct the domain is D: [–5, 7], and the range is R: [–5, 1]

What is an ellipse?

An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.

We have an ellipse equation:

$\rm x^{2}+4y^{2}-2x+16y-19=0$

We can write the above equation as:

$\rm \dfrac{\left(x-1\right)^{2}}{36}+\dfrac{\left(y+2\right)^{2}}{9}=1$

The domain will be:

D: [–5, 7]

The range will be:

R: [–5, 1]

Thus, the option second D: [–5, 7]; R: [–5, 1] is correct the domain is D: [–5, 7] and the range is R: [–5, 1]

Learn more about the ellipse here:

https://brainly.com/question/19507943

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