__Example 1__Find the value of p for which $8y=x+2p$ is a tangent to the curve $2{y}^{2}=x+p$ .

*Nature of the roots (Combination Straight Line and the Curve)*

Onlinetuition.com SPM Additional Mathematics

Find the value of p for which $8y=x+2p$ is a tangent to the curve $2{y}^{2}=x+p$ .