If locus of Mid point of chord at $x^{2} + y^{2} = a^{2}$ makes $90^{0}$ at centre is $x^{2} + y^{2} = \frac{a^{2}}{m}$ .Find $m$

Open in App

Solution

Let the midpoint of BC be (h,b)
$\frac{O A}{O B} = s i n 45^{\circ}$
$\sqrt{h^{2} + b^{2}} = \frac{a}{\sqrt{2}}$
Squaring both sides
$h^{2} + b^{2} = \frac{a^{2}}{2}$
Put h = x , b = y
$x^{2} + y^{2} = \frac{a^{2}}{2}$
Comparing with $x^{2} + y^{2} = \frac{a^{2}}{m}$
$m = 2$

Suggest Corrections

Similar questions

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

90^{o}

x^{2} + y^{2} = a^{2}

2 α

x^{2} + y^{2} = a^{2}

2 α

(c, 0)

x^{2} + y^{2} = a^{2} i s x^{2} + y^{2} - c x = \frac{1}{m} (a^{2} - c^{2})

m

Find the locus the mid-point of focal chords of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 ?$

Join BYJU'S Learning Program