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CBSE Class 10 Answered

sir
Asked by hemant2020 | 04 Nov, 2010, 06:24: PM
answered-by-expert 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 | 04 Nov, 2010, 09:54: PM

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