Oxford University MAT 2018 Solved Papers

Question : 9 of 10

Marks: +1, -0

A sketch of the curve

(x^8+4 y x^6+6 y^2 x^4+4 y^3 x^2+y^4)^2=1

is given below in

Solution:

Note that

x^8+4 x^6 y+6 x^4 y^2+4 x^4 y^3+y^4=(x^2+y)^4

. So the equation is

(x^2+y)^8=1

, which has solutions when

y=1-x^2

or when

y=-1-x^2

. This is a pair of parabolas, and

y

is negative for large

x

in either case. The answer is (c).

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