Question

Two distinct parabolas have the same focus and coordinate axes as their directrices respectively, then slope of their common chord is

• A. $\pm 1$
• B. $\frac{3}{4}$ and $-\frac{4}{3}$
• C. $-\frac{3}{4}$ and $\frac{4}{3}$
• D. $0$ and not defined

Answer 1

The correct option is A $\pm 1$

Given that,

Two parabola have the same focus.

let the focus be $(a,b)$

Now,

Equation of parabola with focus $(a,b)$ and directrix is $y-$axis.

$(x-a{)}^2+(y-b{)}^2=x^2-------\left(1\right)$

Equation of parabola with focus $(a,b)$ and directrix is $x-$axis.

$(x-a{)}^2+(y-b{)}^2=y^2-------\left(2\right)$

By equation $\left(1\right)$ and $\left(2\right)$ to

$x^2=y^2$

$y^2=x^2$

$y=\pm x$

Hence slope $=\pm 1$ this is the answer.