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JEE Previous Year Question

$x = 4 (1 + cos θ) and y = 3 (1 + sin θ) are the parametric equations of$

Topic: JEE PYQ

Answer: D. Full step-by-step solution below.

A $\frac{( x - 3 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{16} = 1$
B $\frac{( x + 4 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{9} = 1$
C $\frac{( x - 4 ) ^{2}}{16} - \frac{( y - 3 ) ^{2}}{9} = 1$
D $\frac{( x - 4 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{9} = 1$

Correct answer: D

Solution

(d) : If x = 4 + 4 cos θ} The parametric equation implies that cos θ = \frac{x - 4}{4} and sin θ = \frac{y - 3}{3} ∴ 1 = cos^{2} θ + sin^{2} θ, or, 1 = (\frac{x - 4}{4})^{2} + (\frac{y - 3}{3})^{2} i.e. \frac{( x - 4 ) ^{2}}{16} + \frac{( y - 3 ) ^{2}}{9} = 1 .

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