Questions
a
ab sq. units
b
a2+b22 sq. units
c
(a+b)22 sq. units
d
a2+ab+b23 sq. units
detailed solution
Correct option is A
Any tangent to the ellipsex2a2+y2b2=1 at P(acosθ,bsinθ) is given byxcosθa+ysinθb=1 It meets the coordinate axes at A(asecθ,0) and B(0,bcosecθ) . Therefore, Area of ΔOAB=12×asecθ×bcosecθ or Δ=absin2θ For area to be minimum, sin2θ should be maximum and we know that the maximum value of sin2θ is 1 . Therefore, Δmax=abTalk to our academic expert!
Similar Questions
Let P be any point on the directrix of an ellipse of eccentricity e. S be the corresponding focus and C the centre of the ellipse. The line PC meets the ellipse at A. the angle between PS and tangent at A is , then is not equal to
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