Find the locus of the mid - points of two parallel chords of the parabola $y^{2} = 4 a x$ which pass through a given point $(α, β)$

y = \frac{2 a}{m}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

y = \frac{4 a}{m}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

y = \frac{6 a}{m}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

y = \frac{8 a}{m}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $y = \frac{2 a}{m}$
We know that the equation of the chord whose mid - point is $(h, k)$ is
$k (y - k) = 2 a (x - h)$
Since the chords are parallel their slope
$\frac{2 a}{k} = c o n s t a n t = m,$ say
Hence the locus of mid - point is $\frac{2 a}{y} = m,$ or $y = \frac{2 a}{m}$ which is a line parallel to the axis of the parabola.
Ans: A

Suggest Corrections

Similar questions

P Q

y^{2} = 4 a x

y = x,

P

Q

y^{2} = 4 a x

y^{2} = 4 a x

P Q

y^{2} = 4 a x

y = x

P

Q

y^{2} = 4 a x

Join BYJU'S Learning Program