Question

when the origin is shifted to the point (5,-2) then the transformed equation of the curve xy+2x-5y+11=0​

Answer 1

X = 5

Y = -2

(5)(-2) + 2(5) - 5(-2) + 11 =0

-10 + 10 + 10 + 11 = 0

21 NOT EQUAL TO 0

THEREFORE, IT IS FALSE

Answer 2

Answer:

When the origin is shifted to the point (5,-2) then the transformed equation of the curve xy+2x-5y+11=0 is XY+4X+21=0.

Step-by-step explanation:

• Let the origin is shifted to a point P ( h , k ). If O( x , y ) is coordinate of origin of old axes and O' ( X , Y ) be coordinate of origin of new axes. Then, x = X + h and y = Y + k .

Given that :

• Origin is shifted to ( 5 , -2 ).
• Equation of curve is xy + 2x - 5y + 11 = 0 .

Solution :

• Let, the origin of new transformed axes be O' (5,-2).
• The new transformed equation is given by putting x= (X + 5) and y = ( Y + 2 ) in transformed equation.

$(X + 5)( Y + 2 )+2(X + 5)-5( Y + 2 )+11=0 \\ </p><p>XY+2X+5Y+10+2X+10-5Y-10+11=0 \\ </p><p>XY+4X+21=0$

• Hence, new transformed equation is XY+4X+21=0 .