Answer
See explanation
Work Step by Step
Given,
z=x^2+9y^2
& k=0,1,2,3,4
for k=1,2,3,4, you will get an ellipse
Let,
z=k=0,1,2,3,4
for k=0
x^2+9y^2=0
for k=1
x^2+9y^2=1 [Ellipse standrad equation x^2/a^2 + y^2/b^2 = 1]
=>x^2+y^2/ (1/3)^2=1
for k=2
x^2+9y^2=2
=>x^2/ (sqrt 2)^2 +y^2/ {(sqrt 2)/3}^2=1
for k=3
x^2+9y^2=3
=>x^2/ (sqrt 3)^2 +y^2/ {(sqrt 3)/3}^2=1
for k=4
x^2+9y^2=4
=>x^2/ (2)^2 +y^2/ (2/3)^2=1
