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[sanju09]

If x = a s, y = b t, and c is such that c = s/t and also s^2 + c^2 = 1; then which of the following is the correct relation between x, y, a, and b?
(A) y √ (a^2 + x^2) = b x
(B) y √ (a^2 - x^2) = b x
(C) y √ (x^2 - a^2) = b x
(D) y √ (b^2 - x^2) = a x
(E) y √ (b^2 + x^2) = a x

[kstv]

Getting nowhere , plugging values seems better
s²+c²=1 so assume s=1/√ 3 and c =√ (2/3 ) have to choose at diff. values as possible
c=s/t so t = s/c = 1/√ t
y=bt so if b =√ 2, y = 1 better to have the value of y as 1
x=as so if a = 3 , x = √ 3
(A) y √ (a^2 + x^2) = b x => y √ (a^2 + x^2) = 1√(9+3) but bx = √6
(B) y √ (a^2 - x^2) = b x => y √ (9-3) = bx = √6
(C) y √ (x^2 - a^2) = b x
(D) y √ (b^2 - x^2) = a x
(E) y √ (b^2 + x^2) = a x=> √(2+3) ,ax =3 √3
The eq are pretty

IMO B