Question

If origin is shifted to (-2,3) then transformed equation of curve ${{x}^{2}}+2y-3=0$ w.r.t. (0,0) is
a)${{x}^{2}}-4x+2y+4=0$
b)${{x}^{2}}-4x-2y-5=0$
c)${{x}^{2}}+4x+2y-5=0$
d)None of these

Answer 1

Hint: In this given question, we can use the equation for transformation of the equation of a curve under the shift of origin in order to solve this question. In doing so, we should use the negatives of the given values of the new abscissa and ordinate added to x and y respectively in places of x and y respectively in the given equation so as to get the required new transformed equation of the given curve.

Complete step-by-step answer:

In this given question, we are asked to find the transformed equation of curve ${{x}^{2}}+2y-3=0$ w.r.t. (0,0) if origin is shifted to (-2,3).
Here, in order to get our needed answer, we are going to use the equation for transformation of the equation of a curve under the shift of origin. In this method we will be adding the negatives of the abscissa and ordinate of the new point (-2,3), with x and y respectively that are (x+2) and (y-3) and then using them in places of x and y respectively in the given equation ${{x}^{2}}+2y-3=0$ and we will get our answer automatically by simplifying the new equation.
The process is as follows:
By putting (x+2) and (y-3) in places of x and y respectively in ${{x}^{2}}+2y-3=0$, we get
\[{{\left( x+2 \right)}^{2}}+2\left( y-3 \right)-3=0\]
Or, \[{{x}^{2}}+4+4x+2y-6-3=0\]
Or, \[{{x}^{2}}+4x+2y-5=0\]
Hence, we get our answer as ${{x}^{2}}+4x+2y-5=0$.
Therefore, the correct option to this given question as obtained is option (c) ${{x}^{2}}+4x+2y-5=0$.

Note: In this type of questions, we must be careful while adding the abscissa and ordinate of the new point to where the origin is shifted to the given variables (x and y) in the equation, they should be in negative of the given form and not as given in the question.