Question

Find the abscissa of a point whose ordinate is $8$ and which is at a distance of $10$ units from $(10,0)$

• A. $4,16$
• B. $2,8$
• C. $4,8$
• D. $2,16$

Answer 1

Answer: (A)

$4,16$

Let the abscissa of the points be $x$. So, the points will be $(10,0)$ and $(x,8)$ .

By using the distance formula,

$\begin{array}{cc}\sqrt{{(10-x)}^2+{(0-8)}^2}& =10\\ 100+x^2-20x+64& =100\\ x^2-20x+64& =0\\ x^2-16x-4x+64& =0\\ x(x-16)-4(x-16)& =0\\ (x-16)(x-4)& =0\\ x-16=0\text{or}x-4& =0\\ x=16\text{or}x& =4\end{array}$

So, option $A$ is correct.