find the pole of the line lx+my+n=0 w.r.t. the ellipse x^2/a^2 + y^2/b^2 = 1
Answer (1)
30th Dec, 2019
Let (x1, y1) be the pole of line lx + my + n = 0. ...... (1)
w.r.t. the ellipse x^2/a^2 + y^2/b^2 = 1 ...... (2)
Now the polar of (x^1, y^1) w.r.t. (2) is x*x1/a^2 + y*y1/b^2 = 1 ...... (3)
Since (1) and (3) represents the same polar, so comparing them we have
(x1/a2)/l + (y1/b2)/b2 = (-1)/n
or x1 = ((-a^2)*l) /n and y1 = ((-b^2)*m) /n
.·. The required pole is ( ((-a^2)*l)/n , ((-b^2)*m)/n )
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