Distribution change using constant

I have these normal distribution

X~N(-1,2)

Y~N(2,3)

X and Y are independent


Find the constant a1,a2,b1,b2 such that

a1*(X-b1)^2 + a2*(Y-b2)^2

become a chi-square (2)



Find the constant c,d1,d2 such that

c(Y-d1) / |X-d2|

become a t-student (1)
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