Question
Ask by Bush Garza. in Mexico
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
La ecuación
representa una elipse centrada en
. Tiene un eje mayor de 2 unidades verticalmente y un eje menor de aproximadamente 1.414 unidades horizontalmente.
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The Deep Dive
Did you know that the equation you provided represents an ellipse? In this case, it is centered at the point (1, 0.5) with a semi-major axis of 2 (along the y-axis, since 4 is under
) and a semi-minor axis of 1 (along the x-axis, since 2 is under
). This shape can be found in various fields, such as astronomy when modeling planetary orbits!
When working with conic sections like ellipses, one common mistake is misidentifying the axes. Remember, the denominators tell you the lengths of the axes; the larger value corresponds to the major axis. Also, be cautious with the orientation! The major axis aligns with the variable that has the larger denominator, as it does here with the
term indicating vertical elongation. Happy graphing!