Bullet-nose curve

In mathematics, a bullet-nose curve is a unicursal quartic curve with three inflection points, given by the equation:$a^2y^2-b^2x^2=x^2y^2\; ,$

The bullet curve has three double points in the real projective plane, at x=0 and y=0, x=0 and z=0, and y=0 and z=0, and is therefore a unicursal (rational) curve of genus zero.

If :$f(z)\; =\; sum\_\{n=0\}^\{infty\}\; \{2n\; choose\; n\}\; z^\{2n+1\}\; =\; z+2z^3+6z^5+20z^7+cdots$then:$y\; =\; fleft(frac\{x\}\{2a\}\; ight)pm\; 2b$are the two branches of the bullet curve at the origin.

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