Answer to Question #115001 in Analytic Geometry for Lizwi

Question

Which of the following is an ellipse? More than one answer may be correct.
A. x^2÷3^2+y^2÷3^2=1
B. x^2=−y
C. y^2=4(1−x^2)
D. None of the above

Answer 1

Which of the following is an ellipse? More than one answer may be correct.

A. x^2÷3^2+y^2÷3^2=1

B. x^2=−y

C. y^2=4(1−x^2)

D. None of the above

Solution:

A.

x^2÷3^2+y^2÷3^2=1

(x^2+y^2)÷9=1

x^2+y^2=9

B.

x^2=−y

C.

y^2=4(1−x^2)

y^2=4-4x^2

y^2+4x^2=4

Answer:

A. x^2÷3^2+y^2÷3^2=1 and C. y^2=4(1−x^2) are ellipses