Asked by hemant2020 | 4th Nov, 2010, 06:24: PM

Expert Answer:

Dear Student,

The equation of any circle can be converted into the standard form by appropriate translation of coordinate axes.
Let the standard equation of the circle be
x2 + y2 = r2.
Its centre is at origin.
The equation of tangent at any point (x1, y1) on the circle is
x1x + y1y = r2

The equation of the normal is of the form
y1x – x1y = k
Point (x1, y1) lies on it
=> y1x1 – x1y1 = k
=> k = 0.
Hence equation of the normal at the point (x1, y1) on the circle is
y1x – x1y = 0 which always passes through the centre irrespective of the coordinates of the contact point (x1, y1)
Hence, the perpendicular to the point of contact to the tangent to a circle passes through the center of the circle.
Hence proved
Regards Topperlearning.

Answered by  | 4th Nov, 2010, 09:54: PM

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