Unattributed TMUA Mock Set A Paper 1 · Question 20

There are many beautifully shaped and meaningful curves in mathematics, and the curve $C$ :

x^2+y^2=1+|x|y

is one of them. Consider the following three statements:

I. The curve $C$ passes through exactly 6 points whose horizontal and vertical coordinates are both integers.
II. The distance from any point on the curve $C$ to the origin does not exceed $\sqrt2$ .
III. The area of the heart-shaped region enclosed by the curve $C$ is less than 3.

How many of these statements are true?

ANone of them

1

2

3

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