AP EAMCET · Maths · Ellipse
The coordinates of a point, in the parametric form, on the ellipse whose foci are \((-1,0)\) and \((7,0)\) and eccentricity \(\frac{1}{2}\), are
- A \((8 \cos \theta, 4 \sqrt{3} \sin \theta)\)
- B \((3+8 \cos \theta, 4 \sqrt{3} \sin \theta)\)
- C \((3+4 \sqrt{3} \cos \theta, 8 \sin \theta)\)
- D \((3+4 \cos \theta, 2 \sqrt{3} \sin \theta)\)
Answer & Solution
Correct Answer
(B) \((3+8 \cos \theta, 4 \sqrt{3} \sin \theta)\)
Step-by-step Solution
Detailed explanation
\( (h,k) = \left( \frac{-1+7}{2}, \frac{0+0}{2} \right) = (3,0) \) \( 2c = 7 - (-1) = 8 \Rightarrow c = 4 \) \( e = \frac{c}{a} \Rightarrow \frac{1}{2} = \frac{4}{a} \Rightarrow a = 8 \) \( b^2 = a^2 - c^2 = 8^2 - 4^2 = 64 - 16 = 48 \Rightarrow b = \sqrt{48} = 4\sqrt{3} \)…
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