If locus of a point, whose chord of contact with respect to the circle $x^{2} + y^{2} = 4$ is a tangent to the hyperbola $x y = 1$ is $x y = c^{2}$ , then value of $c^{2} =$

Open in App

Solution

Let the point be $(h, k)$ .
Then equation of the chord of contact is
$h x + k y = 4$

any tangent to $x y = 1$ is
$\frac{x}{t} + y t = 2$
on comparison, we get
$\frac{2}{t} = h, 2 t = k \Rightarrow k h = 4$
Hence locus will be
$x y = 4$
$∴ c^{2} = 4$

Suggest Corrections

Similar questions

x^{2} + y^{2} = 4

x y = 1

x^{2} + y^{2} = 4

x y = 1

x^{2} - y^{2} = 4

x y = - c^{2}

x y = - c^{2}

t, t

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

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

(α, β)

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

x^{2} + y^{2} = c^{2},

(α, β)

Join BYJU'S Learning Program