Question 1:What does the equation become when the axes are transferred to parallel axes through the point ?

Answer:

Hence the equation gets transformed to

Question 2: What does the equation become if the origin is shifted to the point without rotation?

Answer:

Question 3: Find what the following equations become when the origin is shifted to the point ?

Answer:

Question 4: At what point the origin be shifted so that the equation does not contain any first degree term and constant term?

Answer:

Let the origin be shifted to .

Therefore

For the equation to be free of 1st degree term and constant term we get

Also satisfies .

.

Question 5: Verify that the area of the triangle with vertices remains invariant under the translation of axes when the origin is shifted to the point .

Answer:

with vertices

Now we shift the origin to

Therefore the new vertices or

Therefore

Hence the area of the triangle would remain invariant.

Question 6: Find, what the following equations become when the origin is shifted to the point .

Answer:

Hence the equation become when origin is shifted to

Hence the equation become when origin is shifted to

Hence the equation become when origin is shifted to

Hence the equation become when origin is shifted to

Question 7: Find the point to which the origin should be shifted after a translation of axes so that the following equations will have no first degree terms:

Answer:

i) Let the origin be shifted to .

Therefore

For this equation to be free of terms containing we must have

Hence the origin should be shifted to

ii) Let the origin be shifted to .

Therefore

For this equation to be free of terms containing we must have

Hence the origin should be shifted to

iii) Let the origin be shifted to .

Therefore

For this equation to be free of terms containing we must have

Hence the origin should be shifted to

Question 8: Verify that the area of the triangle with vertices remains invariant under the translation of axes when the origin is shifted to the point .

Answer:

with vertices

Now we shift the origin to

Therefore the new vertices

Hence the area of the triangle would remain invariant.