If f1 and f2 be the feet of the perpendicular from foci s1 and s2 of an ellipse (x²/5) + (y²/3) =1 on the tangent at any point P on the ellipse, then (s1f1)(s2f2) is equal to ?
Ans --3
Any tangent to the ellipse has equation y = mx +
And the foci have the coordinate as S1( ae , 0) and S2 (-ae , 0)
Let the distance from S1 to the tangent be f1 and S2 to the tangent be f2
So S1f1 =
And S2f2 =
So the product of (S1f1)*(S2f2) =
Hence b2 = 3 (ans)
And the foci have the coordinate as S1( ae , 0) and S2 (-ae , 0)
Let the distance from S1 to the tangent be f1 and S2 to the tangent be f2
So S1f1 =
And S2f2 =
So the product of (S1f1)*(S2f2) =
Hence b2 = 3 (ans)