# Need clarity on plotting the y cordinate from the x co-ordinate in Elliptic curve cryptography

I'm just new to elliptic curve cryptography. I have been working on RSA for quite some time. Moreover I'm not from a mathematical background. The whole concept looks very complex. So tell me my understanding is correct or not. I was looking at sample implementation at http://www.enggjournals.com/ijcse/doc...
In the pdf given there,
the curve equation is y^2=x^3+ax+b,the domain parameters are p(751),a(-1),b(188),n(727).
I want to encode a letter 'b' and it is first encoded as 11.
Now x=mk+1 ie 11*20+1=221 cannot solve it for a y such that y^2= x^3 + ax+ b mod p.

So go for x=mk+2 , x=222 , no y exists. x=mk+3, x=223, no y exists.
x=mk+4 so x=224 can solve it for y and y=248

1)Can somebody explain how exactly x=224 solves the equation for y?

2)On what basis mk+1 is taken? Is there any standard formula for choosing the y co-ordinate?

How exactly is this related to sagemath?

If it is not related to sagemath perhaps a better site for your question would be here.