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
Let P(h, k) be the point of intersection of the given lines.
Then, hcos? + ksin? = a
hsin? kcos? = b
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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