39Reflection formula I believe. Its an extension of finding the foot of a perpendicular.
This is a step of a question. I already solved the question by another method but I am confused over which formula is applied directly here :
The image (h,k) of (t2,2t) in x-y+1=0 is given by
h-t2/1 = k-2t/-1 = -2(t2-2t+1)/(1+1)
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7 Answers
39
1Everything is fine except the second last step.
Is this some property-
If a/b = c/d then a/b=c/d=(ab+cd)/(b2+d2) ??
39Rather if a/b = c/d, a/b = c/d = (a² + c²)/(ab + cd). You can multiply multipliers to the fraction and add it in that fashion...I remember doing it in Lagrange differential equations. Can't really say what the property is..
36seems a typical question. can't prove it from L.H.S
i m just proving it by general method...
a/b = c/d = k (say)
=> a = bk and c = dk
Now, (ab + cd)/(b2 + d2) = [bk(b) + d(dk)]/(b2 + d2] = (b2k + d2k) / b2 + d2
= k (b2 + d2)/(b2 + d2) = k = a/b = c/d
Thus, a/b = c/d = (ab + cd)/(b2 + d2)
i know u didn't want it. But this is the end of my thinking capacity now. its too hot in here.
can't think of some other way now. :D