If x and y are connected parametrically by the equations x - acos- y - bcos- without eliminating the parameter find dydx-

Given: nbsp;x = a cosθ, y = b cosθ Finding dyd θ y = b cosθ dyd θ = d(b cosθ)d θ dyd θ = b. ( sinθ) = b sinθ Finding dxd θ x = a cosθ dxd θ = d(a cosθ)d θ d ...

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Standard VII

History

Southern Campaigns

If x and y ar...

Question

If $x$ and $y$ are connected parametrically by the equations $x = a cos θ, y = b cos θ$ without eliminating the parameter find $\frac{d y}{d x} .$

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Solution

Given: $x = a cos θ, y = b cos θ$
Finding $\frac{d y}{d θ}$
$y = b cos θ$
$\frac{d y}{d θ} = \frac{d (b cos θ)}{d θ}$
$\frac{d y}{d θ} = b . (- sin θ) = - b sin θ$

Finding $\frac{d x}{d θ}$
$x = a cos θ$
$\frac{d x}{d θ} = \frac{d (a cos θ)}{d θ}$
$\frac{d x}{d θ} = a . (- sin θ) = - a sin θ$

Finding $\frac{d y}{d x}$
Now, $\frac{d y}{d x} = \frac{\frac{d y}{d θ}}{\frac{d x}{d θ}} \dots (i)$
Substituting the value of $\frac{d y}{d θ}$ and $\frac{d x}{d θ}$ in (i) we get,
$\frac{d y}{d x} = \frac{- b sin θ}{- a sin θ} = \frac{b}{a}$

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Southern Campaigns

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If x and y are connected parametrically by the equations x=acosθ,y=bcosθ without eliminating the parameter find dydx.

If $x$ and $y$ are connected parametrically by the equations $x = a cos θ, y = b cos θ$ without eliminating the parameter find $\frac{d y}{d x} .$