Question

If the origin is shifted to the point (h,k), the point (x, y) (X,Y) may changed to then (h,k) =​

Answer 1

It is called plasmolysis. When a plasmolysed cell is placed in a hypotonic solution, (i.e., the solution having solute concentration lower than the cell sap), the water moves into the cell because of the higher concentration of water outside the cell than in the cell. The cell then swells to become turgid.

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Answer 2

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.