Eliminate ø from the following
x= a cos ø, y = b sin ø
Answers
Answered by
4
\begin{lgathered}\bold{\frac{x}{a}cos\theta+\frac{y}{b}sin\theta=1-----(1)}\\\\\bold{\frac{x}{a}sin\theta-\frac{y}{b}cos\theta=1-----(2)}\end{lgathered}
a
x
cosθ+
b
y
sinθ=1−−−−−(1)
a
x
sinθ−
b
y
cosθ=1−−−−−(2)
Squaring both the equations and then adding ,
\bold{[\frac{x}{a}cos\theta+\frac{y}{b}sin\theta]^2+[\frac{x}{a}sin\theta-\frac{y}{b}cos\theta]^2=1^2+1^2}[
a
x
cosθ+
b
y
sinθ]
2
+[
a
x
sinθ−
b
y
cosθ]
2
=1
2
+1
2
x²/a² cos²θ + y²/b² sin²θ + 2xy/ab sinθ.cosθ + x²/a² sin²θ + y²/b² cos²θ - 2xy/ab sinθ.cosθ = 2
⇒x²/a² (cos²θ + sin²θ) + y²/b² (sin²θ + cos²θ ) = 2
⇒x²/a² × 1 + y²/b² × 1 = 2 [ ∵ sin²x + cos²x = 1 from trigonometric identities ]
∴ x²/a² + y²/b² = 2 , hence proved
Answered by
9
Hey mate,
see the Æñßwéí in photo
Give ❤️ plz
Attachments:
Similar questions