Shift of Origin

The origin is shifted to $\left(2,3\right)$ by the translation of axes. If the coordinates of a point $P$ change as $\left(0,0\right)$, find the coordinates of $P$ in the original system.

The origin is shifted to $\left(2,3\right)$ by the translation of axes. If the coordinates of a point $P$ change as $\left(-4,3\right)$, find the coordinates of $P$ in the original system.

The origin is shifted to $\left(2,3\right)$ by the translation of axes. If the coordinates of a point $P$ change as $\left(4,5\right)$, find the coordinates of $P$ in the original system.

When the origin is shifted to $(4,-5)$ by the translation of axes, find the coordinates of the $\left(4,-5\right)$ with reference to new axes.

When the origin is shifted to $(4,-5)$ by the translation of axes, find the coordinates of the $\left(-2,4\right)$ with reference to new axes.

When the origin is shifted to $(4,-5)$ by the translation of axes, find the coordinates of the $\left(0,3\right)$ with reference to new axes.

If origin is shifted to $\left(h,k\right)$, so that the linear (one degree) terms in the equation $x^2+y^2-4x+6y-7=0$ are eliminated. Then the point $\left(h,k\right)$ is

The new coordinates of a point $\left(4,5\right),$ when the origin is shifted to the point $\left(1,-2\right)$ are

If the equation $x^2+y^2-4x-6y-12=0$ is transformed to $X^2+Y^2=25$ when the axes are translated to a point then the new coordinates of (-3, 5) are

Without changing the direction of coordinate axes, origin is transferred to (h, k), so that the linear (one degree) terms in the equation $x^2+y^2-4x+6y-7=0$ are eliminated. Then the point (h, k) is

The new coordinates of a point $\left(4,5\right)$, when the origin is shifted to the point $\left(1,-2\right)$ are

If the coordinate axes are shifted to the point $\left(-1,\mathrm{ }2\right)$ without rotation, then the curve whose equation is $2{\mathrm{x}}^2+{\mathrm{y}}^2-4\mathrm{x}+4\mathrm{y}=0$ will have the equation -

Without changing the direction of coordinate axes, origin is transferred to $\left(\mathrm{h},\mathrm{ }\mathrm{k}\right)$ , so that the linear (one degree) terms in the equation ${\mathrm{x}}^2+{\mathrm{y}}^2-\mathrm{ }4\mathrm{x}+6\mathrm{y}-\mathrm{ }7=0$ are eliminated. Then the point $\left(\mathrm{h},\mathrm{ }\mathrm{k}\right)$ is -

The new coordinates of a point $\left(4,\mathrm{ }5\right)$ , when the origin is shifted to the point $\left(1,\mathrm{ }-2\right)$ are

If origin is shifted to $\left(2,-3\right)$ then transformed equation of curve $x^2+2y-3=0$ is

Without changing the direction of coordinate axes, origin is transferred to $\left(h, k\right)$ so that the linear (one degree) terms in the equation $x^2+y^2-4x+6y+7=0$ are eliminated. Then the point $\left(h, k\right)$ is

The new coordinates of a point $\left(4,\mathrm{ }5\right)$ , when the origin is shifted to the point $\left(1,\mathrm{ }-2\right)$ are

In order to eliminate the first degree terms from the equation $2x^2+4xy+5y^2-4x-22y+7=0,$ the point to which origin is to be shifted, is