Find the transformed equation of 2x square+4xy+5y square=0 when origin is shifted to (3,4)
Answers
Given : 2x² + 4xy + 5y²
To find : transformed equation when origin is shifted to (3,4)
Solution:
2x² + 4xy + 5y²
origin is shifted to (3,4)
=> X = x - 3 hence x = X + 3
& Y = y - 4 hence y = Y + 4
Substituting
2(X + 3)² + 4(X+3)(Y+4) 5(Y+ 4)²
= 2(X² + 6X + 9 ) + 4(XY + 4X + 3Y + 12) + 5(Y² + 8Y + 16)
= 2X² + 12X + 18 + 4XY + 16X + 12Y + 48 + 5Y² + 40Y + 80
= 2X² + 5Y² + 4XY + 28X + 52Y + 146
2X² + 5Y² + 4XY + 28X + 52Y + 146 is the transformed equation
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