Find the minimum distance between the curves (Y - 2)² = 8(X - 4.5) and (X - 4)² = 4(Y - 6)

Asked Apr 01 '15 at 11:53

Active Apr 01 '15 at 11:53

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Find the minimum distance between the curves (Y - 2)² = 8(X - 4.5) and (X - 4)² = 4(Y - 6)

Attempt:- The minimum distance between these two parabolas lies along their common normal.

Relevant equations:-

Normal to C1: Y - 2 = M1 (X - 4.5) - 4 M1 - 2 M1³

Normal to C2: X - 4 = M2 (Y - 6 ) - 2 M2 - 2 M2³ Since these both equations represent the same line, comparing the coefficients of X and Y we get,

M1 * M2 =1

2.- 8.5 M1 - 2 M1³ +2 = -4 / M2 + 2 M2² + 8

asked Apr 01 '15 at 11:53

miyagi_do

1,663

See http://math.stackexchange.com/questions/1209893/minimum-distance-between-two-parabolas – lab bhattacharjee Apr 01 '15 at 11:56
There we have symmetry between the curves and i need to this using co normals – miyagi_do Apr 01 '15 at 13:21

Find the minimum distance between the curves (Y - 2)² = 8(X - 4.5) and (X - 4)² = 4(Y - 6)

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