Question 54.
Let P be a variable point on the ellipse x^2/a^2+y^2/b^2=1 with foci S(1) and S(2).If A be the area of the triangle PS(1)S(2),then find the maximum value of A.
Answer 54.
S(1) = (ae, 0), S(2) = (-ae, 0)
By symmetry, area is maximum when P = (0, b)
Shifting origin to (0, b),
S(1) = (ae, -b) and S(2) = (-ae, -b) and P (0, 0)
=> area A
= (1/2) modulus of determinant
l ae - b l
l-ae - b l
= (1/2) l -abe -abe l
= abe.
LINK to YA!
Let P be a variable point on the ellipse x^2/a^2+y^2/b^2=1 with foci S(1) and S(2).If A be the area of the triangle PS(1)S(2),then find the maximum value of A.
Answer 54.
S(1) = (ae, 0), S(2) = (-ae, 0)
By symmetry, area is maximum when P = (0, b)
Shifting origin to (0, b),
S(1) = (ae, -b) and S(2) = (-ae, -b) and P (0, 0)
=> area A
= (1/2) modulus of determinant
l ae - b l
l-ae - b l
= (1/2) l -abe -abe l
= abe.
LINK to YA!
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