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10.2 parabola,ellipse,hyperbola — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS10.2 parabola,ellipse,hyperbola1 Mark
MCQ
The equation of the ellipse whose one focus is at $(4, 0)$ and whose eccentricity is $4/5$, is
  • A
    $\frac{{{x^2}}}{{{3^2}}} + \frac{{{y^2}}}{{{5^2}}} = 1$
  • ✓
    $\frac{{{x^2}}}{{{5^2}}} + \frac{{{y^2}}}{{{3^2}}} = 1$
  • C
    $\frac{{{x^2}}}{{{5^2}}} + \frac{{{y^2}}}{{{4^2}}} = 1$
  • D
    $\frac{{{x^2}}}{{{4^2}}} + \frac{{{y^2}}}{{{5^2}}} = 1$
✓

Answer

Correct option: B.
$\frac{{{x^2}}}{{{5^2}}} + \frac{{{y^2}}}{{{3^2}}} = 1$
b
(b) Here $ae = 4 $and$ e = \frac{4}{5} \Rightarrow a = 5$

Now ${b^2} = {a^2}(1 - {e^2}) \Rightarrow {b^2} = 25\left( {1 - \frac{{16}}{{25}}} \right) = 9$

Hence equation of the ellipse is $\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{9} = 1$.

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