The maximum value of the area of the triangle with vertices a- 0 acos- bsin- and acos- - bsin- is

The correct option is A 3√(3)ab/4 area of Δ=12a #160; amp; 0 a #160; cosθ #160; amp; b sinθ a #160; cosθ #160; amp; b #1 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Inverse of a Matrix

The maximum v...

Question

The maximum value of the area of the triangle with vertices $(a, 0) (a cos θ, b sin θ)$ and $(a cos θ, - b sin θ)$ is

\frac{3 \sqrt{3} a b}{4}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\sqrt{a b}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{\sqrt{3 a b}}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{3 a b}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{3 \sqrt{3} a b}{4}$
area of $Δ = \frac{1}{2} ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} a & 0 a c o s θ & b s i n θ a c o s θ & - b s i n θ a & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣$
$= \frac{1}{2} ((a b s i n θ - a b s i n θ c o s θ) - (a b s i n θ c o s θ - a b s i n θ))$
$= (a b s i n θ - a b s i n θ c o s θ)$
$f (θ) =$ area of $Δ = a b s i n θ (1 - c o s θ)$
$f^{1} (θ) = c o s θ (1 - c o s θ) + (s i n^{2} θ)$
$= c o s θ - c o s^{2} θ$
$f^{1} (θ) = 0$ when $θ = \frac{2 π}{3}$
max area of $Δ$ is when $θ = \frac{2 π}{3}$

Suggest Corrections

Similar questions

Q. Area of a triangle whose vertices are

(a cos θ, b sin θ), (- a sin θ, b cos θ)

and

(- a cos θ, - b sin θ)

Write the value of $θ ε (\frac{π}{2})$ for which area of the triangle formed by points O(0,0), A $(a c o s θ, b s i n θ)$ and $(a c o s θ, b s i n θ)$ is maximam.

a b + 2 a b^{2} + 3 a b^{3} + 4 a b^{4} + . . . . . .

= ?

Q. Write the value of θ ϵ

(0, \frac{π}{2})

for which area of the triangle formed by points O (0, 0), A (a cos θ, b sin θ) and B (a cos θ, − b sin θ) is maximum.

Q. Simplify:

\frac{12 a b^{3} - 6 a^{2} b}{3 a b}

(given that

a b \neq 0

)

Join BYJU'S Learning Program

The maximum value of the area of the triangle with vertices (a,0)(acosθ,bsinθ) and (acosθ,−bsinθ) is

The maximum value of the area of the triangle with vertices $(a, 0) (a cos θ, b sin θ)$ and $(a cos θ, - b sin θ)$ is