The curve with parametric equations $x = {\rm{\alpha }} + 5\cos {\rm{\theta }},\;y = {\rm{\beta }} + 4\sin {\rm{\theta }}$ (where $\theta $ is parameter) is

JEE MATHEMATICS MCQ: ELLIPSE

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The curve with parametric equations

x = \mathrm{\alpha } + 5\cos \mathrm{\theta },\;y = \mathrm{\beta } + 4\sin \mathrm{\theta }

(where

\theta

is parameter) is

View answer and explanation

Correct option: B

An ellipse

Option B (An ellipse) is correct because the parametric equations describe an ellipse centered at (α, β) with semi-major and semi-minor axes of 5 and 4, respectively.

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\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1

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9 x^{2}+16 y^{2}=144

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\mathrm{PA}+\mathrm{PB}

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\frac{x^2}{25}+\frac{y^2}{16}=1

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