Question
Download Solution PDFThe foci of the ellipse 4x2 + 9y2 = 1 are at Q and R. If P(x, y) is any point on the ellipse, then what is PQ + PR equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given:
4x2 + 9y2 = 1
Here a = 1/2 and b = 1/3
Now
e = \(\sqrt{1-\frac{b^2}{a^2}} = \frac{\sqrt5}{3}\)
foci = (±ae, 0)
= ( ± \((\frac{1}{2}\frac{\sqrt5}{3},0)\)
= (± \(\frac{\sqrt5}{6},0\))
Thus, P(x, y) is any point on the ellipse
⇒ PQ + PR = 2a = 2× 1/2 = 1
∴ Option (b) is correct.
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