Question

The points on the y-axis which are at a distance of 5 units from (4,-1) are

• A. $(0,-2),(0,4)$
• B. $(0,2),(0,4)$
• C. $(0,2),(0,-4)$
• D. $(0,-2),(0,-4)$

Answer 1

The correct option is C $(0,2),(0,-4)$

Let the point is $(0,y)$

$5=\sqrt{(4-0{)}^2+(y+1{)}^2}$

$5=\sqrt{16+(y+1{)}^2}$

$\Rightarrow 25=16+(y+1{)}^2$

$\Rightarrow 25-16=y^2+1+2y$

$\Rightarrow 9=y^2+1+2y$

​​​​​​​$\Rightarrow 8=y^2+2y$

​​​​​​​$\Rightarrow y^2+2y-8=0$

​​​​​​​$\Rightarrow y^2+4y-2y-8=0$

​​​​​​​$\Rightarrow y(y+4)-2(y+4)=0$

​​​​​​​$\Rightarrow (y+4)(y-2)=0$

​​​​​​​$\Rightarrow y=2,y=-4$

Points $=(0,-4),(0,2)$