Question

Select from the following equations describing the set of all points $(x,y)$ in the coordinate plane that are at a distance of $\sqrt{3}$ from the point $(2,-5)$.

• A. $(x-2{)}^2+(y-5{)}^2=3$
• B. $(x-2{)}^2+(y+5{)}^2=3$
• C. $(x+2{)}^2+(y+5{)}^2=3$
• D. $(x+2{)}^2-(y-5{)}^2=3$
• E. $(x-2{)}^2-(y+5{)}^2=3$

Answer 1

The correct option is B $(x-2{)}^2+(y+5{)}^2=3$

Given that point $(x,y)$ is at a distance of $\sqrt{3}$ from the point $(2,-5)$
So we have $\sqrt{{(x-2)}^2+{(y+5)}^2}=\sqrt{3}$
On squaring both sides, we get

${(x-2)}^2+{(y+5)}^2=3$