Solution:
(b) According to the question, the distance between the points \((4, p)\) and \((1,0)=5\)
1. \(\quad \sqrt{(1-4)^{2}+(0-p)^{2}}=5\)
\([\because\) distanca bewwean the pcints
\(\left(x_{1}, y_{1}\right)\) and \(\left.\left(x_{2}, y_{2}\right) d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\right]\)
\(\Rightarrow \quad \sqrt{(-3)^{2}+p^{2}}=5\) \(\Rightarrow \quad \sqrt{9+p^{2}}=5\)
On scuaring both the sides, we pet
$$
\begin{array}{r}
9+p^{2}=25 \\
\Rightarrow p^{2}=16 \Leftrightarrow \rho=\pm 4
\end{array}
$$
Hence, the requred value of \(p\) is \(\pm 4\),
