Eliminate theta...x=a cos theta, y=b sin theta

x=a cos theta, y=b sin theta. 
we know the identities of trigonometry in terms of sin theta and cos theta
sin2K+cos2 K=1, hence we should try to convert the above into  sin2K+cos2 K=1, so as to eliminate the sin theta and cos theta
I think,
x2b2+y2a2 is the correct answer because,
let theta be Z
x2b2+y2a2=a2b 2cos2Z+a2 b2sin2Z

by taking  a2bcommon the identity is used to remove the theta.
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x=a cos theta=> cos theta = x/a            similarly, sin theta= y/b
sin2theta + cos​2theta = 1
=>x2​/a2 + y2/b2 =1
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