Question

The equation of a locus is $(2x-1{)}^2+{(y+\frac{3}{2})}^2=4.$ The origin in shifted to the point $(\frac{1}{2},-\frac{3}{2})$, the axes remaining parallel. Find the equation of the locus in the new system.

Answer 1

Origin being shifted to $(\frac{1}{2},\frac{-3}{2})$

For new system we replace $x\stackrel{}{\to }x-\frac{1}{2}$ and $y\stackrel{}{\to }y+\frac{3}{2}$

$=>{(2(x-\frac{1}{2})-1)}^2+{(y+\frac{3}{2}+\frac{3}{2})}^2=4=>(2x-2{)}^2{(y+3)}^2=4$