If one end of a focal chord AB of the parabola y^2=8x is at A(12,-2), then the equation of…

Question

If one end of a focal chord $AB$ of the parabola $y^2=8x$ is at $A\left(\dfrac12,-2\right)$, then the equation of the tangent to it at $B$ is:

Accepted Answer

$y^2=4(2)x$, $a=2$. Using $(at^2,2at)$: at $A$, $2(2)t_1=-2\Rightarrow t_1=-\frac12$ (and $x=2t_1^2=\frac12$ ).

Focal chord: $t_1t_2=-1\Rightarrow t_2=2$; $B=(2(4),2(2)(2))=(8,8)$.

Tangent at $B$: $8y=4(x+8)\Rightarrow x-2y+8=0.$

Solutions · 1