Question

The point to which the origin should be trans-
lated in order to make the first degree terms
missing in the equation 3x–2x+y=8 = 0 is​

Answer 1

Answer:

Let the origin be shifted to the point (h,k)

Let (x,y) and (x

′

,y

′

) are the coordinates of a point in the old and new system respectively, then x=x

′

+h,y=y

′

+k

So the transformed equation is

2(x

′

+h)

2

+5(x

′

+h)(y

′

+k)+3(y

′

+k)

2

+6(x

′

+h)+7(y

′

+k)+1=0

⇒2x

′

2

+4x

′

h+2h

2

+5x

′

y

′

+5x

′

k+5y

′

h+5hk+3y

′

2

+3k

2

+6y

′

k+6x

′

+6h+7y

′

+7k+1=0

⇒2x

′

2

+3y

′

2

+x

′

(4h+5k+6)+y

′

(5h+6k+7)

+(2h

2

+5hk+6h+7k+3k

2

+1)+5x

′

y

′

=0

In order to remove the first degree terms, we must have 4h+5k+6=0 and 5h+6k+7=0

⇒h=1 and k=−2

∴ the origin must be shifted to the point (1,−2) to remove 1st degree trems from the given equation.

How satisfied

Step-by-step explanation:

hope this helps