Explanation

(b)
Given equation of the curve is
${3x}^{2} - y^{2} - 2x + 4y = 0$ …(i)
Let the equation of one of the chord be
$y = mx + c\ \Rightarrow \ \frac{y - mx}{c} = 1\ldots(ii)$
On making Eq. (i) homogeneous, we get
${3x}^{2} - y^{2} + ( - 2x + 4y)\left( \frac{y - mx}{c} \right) = 0$
$\Rightarrow \ x^{2}(3c + 2m) + y^{2}( - c + 4) - 2xy - 4mxy = 0$
Which represent a pair of straight lines passing through origin. Since, the angle subtended is a right angle.
$\therefore 3c + 2m - c + 4 = 0$
$\Rightarrow c = - m - 2$
Substituting value of $c$ in $y = mx + c,\$we have
$y = mx - m - 2 \Rightarrow y + 2 = m(x - 1)$
⇒ All such chords pass through a fixed point $(1,\ - 2)$