Let A and B be the two points of intersection of the line y+5=0 and the mirror image of th…

Question

Let $A$ and $B$ be the two points of intersection of the line $y+5=0$ and the mirror image of the parabola $y^2=4x$ with respect to the line $x+y+4=0$. If $d$ denotes the distance between $A$ and $B$, and $a$ denotes the area of $	riangle SAB$, where $S$ is the focus of the parabola $y^2=4x$, then the value of $a+d$ is \_\_\_\_\_\_\_\_.

Answer: 14

Accepted Answer

*(The full working for the mirror-image parabola is heavily corrupted in the source; the recoverable final steps give $A,B$ four units apart with the triangle's base $4$ and height $5$.)*

$$a=\text{Area}=\frac12\times4\times5=10,\qquad d=4,\qquad a+d=14.$$

Solutions · 1