Definition of a circle

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Question

The distance between the chords of contact of the tangent to the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$
from the origin and the point $(g, f)$ is

Moderate

Solution

The equations of chords of contact of the tangents drawn from the origin and the point (g, f) to the given circle are respectively
$g x + f y + c = 0$ …(i)
and, $2 g x + 2 f y + g^{2} + f^{2} + c = 0$ …(iii)
Clearly, (i) and (ii) are parallel. Therefore, the distance 'd' between them is given by
$d = \frac{g^{2} + f^{2} + c}{\sqrt{4 g^{2} + 4 f^{2}}} - \frac{c}{\sqrt{8^{2} + f^{2}}} = \frac{g^{2} + f^{2} - c}{2 g^{2} + f^{2}}$

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Definition of a circle

Remember concepts with our Masterclasses.

The distance between the chords of contact of the tangent to the circle x2+y2+2gx+2fy+c=0from the origin and the point (g,f) is

Ready to Test Your Skills?

free study material

The distance between the chords of contact of the tangent to the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$
from the origin and the point $(g, f)$ is