SOLUTION: This is a question involving conic sections. Can someone explain #14 on https://www.math.purdue.edu/php-scripts/courses/oldexams/serve

SOLUTION: This is a question involving conic sections. Can someone explain #14 on https://www.math.purdue.edu/php-scripts/courses/oldexams/serve_file.php?file=16200FE-F2018.pdf ?

Question 1195932: This is a question involving conic sections. Can someone explain #14 on https://www.math.purdue.edu/php-scripts/courses/oldexams/serve_file.php?file=16200FE-F2018.pdf ?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The equation has both x^2 and y^2 terms with both positive, so the conic is an ellipse. There are no linear terms, so the center of the ellipse is at the origin. The standard form is either if the major axis is horizontal or if the major axis is vertical. (For an ellipse, a > b, so a^2 > b^2.)

To put the given equation in standard form, divide the whole equation by 2:

then put the left-hand side in the required form:

Because 1 > 2/3, the major axis is vertical, so the x coordinates of the foci are still 0. That eliminates answer choices A and C.

The distance from the center to each focus is c, where a, b, and c are related by

So the two foci are a distance above and below the center (0,0), giving

ANSWER: D

RELATED QUESTIONS
This is a calculus question involving series. Can you explain #16 on... (answered by ikleyn)

This is a calculus question. Can you explain each choice of #4 on... (answered by ikleyn)

This is a calculus question. Can you explain how to solve #12 on... (answered by math_tutor2020)

This is a calculus question. Could you explain #16 on... (answered by ikleyn)

This is a calculus question involving series. Can someone explain #13 on... (answered by Edwin McCravy,ikleyn)

This is a calculus question. Could you explain question 18 on... (answered by Edwin McCravy,ikleyn)

The positive integers greater than 3 are arranged in rows and columns as illustrated. In... (answered by math_tutor2020,ikleyn)

Can you help me to understand and explain this? Thanks. Conic sections are curves that... (answered by stanbon)

Points A, B, Q, D, and C lie on the circle as shown and the measures of arcs BQ and QD (answered by math_helper)