Question

The points on the y-axis that are at a distance of $10$ units from the point $(8,8)$ are

• A. $(0,-2)$ and $(0,-14)$
• B. $(0,2)$ and $(0,14)$
• C. $(0,2)$ and $(0,-14)$
• D. None of these

Answer 1

Answer: (B)

$(0,2)$ and $(0,14)$

As the point is on $y$-axis, so its co-ordinates are $P=(x_1,y_1)=(0,p)$

Another point is $Q=(x_2,y_2)=(8,8)$

$\therefore$ the distance $PQ=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}=10$

$\Rightarrow \sqrt{{(0-8)}^2+{(p-8)}^2}=10$

$\Rightarrow p^2-16p+128=100$

$\Rightarrow (p-14)(p-2)=0$

$\Rightarrow p=2$ or $14$

$\therefore$ the co-ordinates are $(0,2)$ or $(0,14)$.