Question

The point of contact of the line $x-y+2=0$ with the parabola $y^2-8x=0$ is:`

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

Answer 1

The correct option is A $(2,4)$

The equations are:

Line $x-y+2=0$ parabola $y^2-8x=0$

$x=y-2$

$\therefore$ $y^2-8(y-2)=0$

$y^2-8y+16=0$

$y^2-2\left(4\right)y$ $+4^2=0$

${(y-4)}^2=0$ $\Rightarrow$ $y-4=0$

$\Rightarrow y=4$

$x=4-2=2$

$\therefore$ Point of contact of given line & parabola is $(2,4)$