Question

Select the one equation that describes the set of the points $(x,y)$ in the coordinate plane that are at a distance of $5$ from the point $(-3,4)$.

• A. $(x+3)+(y-4)=5$
• B. $(x-3)+(y+4)=5$
• C. $(x+3{)}^2+(y-4{)}^2=5$
• D. $(x+3{)}^2+(y-4{)}^2=25$
• E. $(x-3{)}^2+(y-4{)}^2=25$

Answer 1

The correct option is D $(x+3{)}^2+(y-4{)}^2=25$

Distance between any two points $(x_1,y_1)$ and $(x_2,y_2)$ is

$|P|=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

Distance from $(-3,4)$ to any point is

$|P|=\sqrt{{(x+3)}^2+{(y-4)}^2}$

The equation which describes the set of points in a co-ordinate plane that are of distance $5$ from point $(-3,4)$ is

$5=\sqrt{{(x+3)}^2+{(y-4)}^2}$

Hence, option D is correct.