the minimum area of triangle formed by tangents to ellipse x^₂/a²+y²/b² =1 and the coordinate axes is

ab

(asquare+bsquare)/2

(a+b)square/2

(asquare+ab+bsquare)/3

Question

the minimum area of triangle formed by tangents to ellipse x
2 /a2+y2/b2
=1 and the coordinate axes is

ab
(asquare+bsquare)/2
(a+b)square/2

(asquare+ab+bsquare)/3

Anuradha Sharma · Accepted Answer

The equation of tangent at acosθ, bsinθ to the ellipse, x2a2+y2b2=1 is given as, xcosθa+ysinθb=1or xasecθ+ybcosecθ=1It meets the coordinate axes at Aasecθ, 0 and B0,bcosecθSo area of the triangle, =12×OA×OB=12×asecθ×bcosecθ=12×absinθcosθ=absin2θNow since sin function has maximum value =1 so Area of triangle= absin2θ≥ab

the minimum area of triangle formed by tangents to ellipse x 2 /a2+y2/b2 =1 and the coordinate axes is ab (asquare+bsquare)/2 (a+b)square/2 (asquare+ab+bsquare)/3

the minimum area of triangle formed by tangents to ellipse x^₂/a²+y²/b² =1 and the coordinate axes is

ab

(asquare+bsquare)/2

(a+b)square/2

(asquare+ab+bsquare)/3