Question

The line $y=-1$ intersects the parabola $y=x^2-10x+24$ at one point. Find the coordinates of the point of the intersection.

• A. $(-5,-1)$
• B. $(0,-1)$
• C. $(5,-1)$
• D. $(24,-1)$
• E. $(35,-1)$

Answer 1

Answer: (C)

$(5,-1)$

Given $y=-1$ intersects parabola at one point, put $y=-1$ in parabola equation

We get $x^2-10x+24=-1$

$\Rightarrow$ $x^2-10x+25=0$

$\Rightarrow$ ${(x-5)}^2=0$
$\Rightarrow$ $x=5$

Therefore, the point of intersection is $(5,-1)$.