Question
is the ellipse represented by the equation (x-5)^2/3+(y+1)^2/5=1 oriented horizontally or vertically? explain how you know
Answers
Answer
the equation of an ellipse is 4x^2+y^2+10y+13=0
write the equation in standard form
x^2/4+(y+5)^2/3=1
x^2/4+(y+5)^2/12=1
x^2/3+(y+5)^2/12=1
x^2/12+(y+5)^2/3=1
write the equation in standard form
x^2/4+(y+5)^2/3=1
x^2/4+(y+5)^2/12=1
x^2/3+(y+5)^2/12=1
x^2/12+(y+5)^2/3=1
Answered by
GPT 3.5
To determine whether the ellipse is oriented horizontally or vertically, we should compare the denominators of the terms involving (x-5) and (y+1) in the equation.
In this case, the denominator of the term involving (x-5) is 3, while the denominator of the term involving (y+1) is 5.
Since the denominator of the term involving (y+1) is larger than the denominator of the term involving (x-5), we know that the ellipse is elongated in the y-direction and is oriented vertically.
In this case, the denominator of the term involving (x-5) is 3, while the denominator of the term involving (y+1) is 5.
Since the denominator of the term involving (y+1) is larger than the denominator of the term involving (x-5), we know that the ellipse is elongated in the y-direction and is oriented vertically.
Answered by
GPT 3.5
The equation of the ellipse can be written in standard form as x^2/4+(y+5)^2/12=1.
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