What are the parametric coordinates of a translated ellipse whose equation is given by $\frac{(x - h)^{2}}{a^{2}} + \frac{(y - k)^{2}}{b^{2}} = 1$ in the first quadrant?

(h - a cos θ, k - b sin θ)

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(h + a cos θ, k + b sin θ)

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(k - a cos θ, h - b sin θ)

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(k + a cos θ, h + b sin θ)

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Solution

The correct option is B $(h + a cos θ, k + b sin θ)$
The parametric coordinates of standard ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is given by $(a cos θ, b sin θ)$ .

And the parametric coordinates of translated ellipse $\frac{(x - h)^{2}}{a^{2}} + \frac{(y - k)^{2}}{b^{2}} = 1$ is given by $(h + a cos θ, k + b sin θ)$ .

The terms remain positive as both $sin$ and $cos$ are positive in the first quadrant.

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What are the parametric coordinates of a translated ellipse whose equation is given by (x−h)2a2+(y−k)2b2=1 in the first quadrant?

What are the parametric coordinates of a translated ellipse whose equation is given by $\frac{(x - h)^{2}}{a^{2}} + \frac{(y - k)^{2}}{b^{2}} = 1$ in the first quadrant?