The locus of the point of intersection of lines xcos alpha + ysin alpha =a and xsin alpha - ycos alpha=b(alpha is a variable) is ________??

Asked by  | 4th Nov, 2013, 11:07: PM

Expert Answer:

Let P(h, k) be the point of intersection of the given lines.
 
Then, hcos? + ksin? = a                                         … (1)
 
        hsin? – kcos? = b                                         … (2)
 
Here a is a variable. So we have to eliminate a.
 
Squaring and adding (1) and (2),
 
(hcos? + ksin?)2 + (hsin? – kcos?)2 = a2 + b2
 
h2 + k2 = a2 + b2
 
Hence, locus of (h, k) is x2 + y2 = a2 + b2.

Answered by  | 4th Nov, 2013, 11:55: PM

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