Question

Two parabolas have the same focus. If their directrices are the $x-$axis & the $y-$axis respectively, then the slope of their common chord is

• A. $1$
• B. $-1$
• C. $\frac{4}{3}$
• D. $\frac{3}{4}$

Answer 1

Answer: (A), (B)

The correct options are
A $-1$
B $1$

$P_1\equiv (x-a{)}^2=4\frac{b}{2}(y-\frac{b}{2})$
$\Rightarrow x^2-2ax+a^2-2yb+b^2=0$
Similarly
$P_2\equiv y^2-2ax-2by+a^2+b^2=0$
Common chord is $P_1-P_2=0$
$\Rightarrow x^2-y^2=0,\Rightarrow (x+y)(x-y)=0$
Clearly slopes are $1,-1.$