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![[Post New]](/templates/default/images/icon_minipost_new.gif) 12 Dec 2007 17:56:02 IST
Accepted Answer [?]
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Tangent at point P(x',y') is xx'/a^2 + yy'/b^2 = 1
now x' ^ 2/ a^2 + y' ^ 2/b^2 = 1 as the point is on the ellipse .
the slope of the tangent is -x'b^2/y'a^2
slope of the line joining the point P and the focus which is farther from the point P is to be found out
point S is ( -ae,0)
Slope of SP is y' / x' + ae
so tan theta = {y' / x'+ae + x'b^2 / y'a^2} / 1- y' x'b^2 / (x' + ae)y'a^2
which on simplifying we get a^2 y'^2 + b^2x'^2 + b^2x'ae / x'y'(a^2 - b^2)
= a^2b^2 + b^2x'ae / x'y'a^2e^2 + a^3ey
=b^2a(a+ex') / a^2ey'(a+ex') = b^2 / aey'
theta is the angle made by the line SP and the tangent .
Hope this helps.
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