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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 tangent and normal to the ellipse $3x^2 + 5y^2 = 32$ at the point $P(2, 2)$ meet the $x-$ axis at $Q$ and $R,$ respectively. Then the area(in sq. units) of the triangle $PQR$ is
  • A
    $\frac {34}{15}$
  • ✓
    $\frac {68}{15}$
  • C
    $\frac {14}{3}$
  • D
    $\frac {16}{3}$
✓

Answer

Correct option: B.
$\frac {68}{15}$
b
$3{x^2} + 5{y^2} = 32$

${\left. {\frac{{dy}}{{dx}}} \right|_{\left( {2,2} \right)}} =  - \frac{3}{5}$

tengent $:y - 2 =  - \frac{3}{5}\left( {x - 2} \right) \Rightarrow Q\left( {\frac{{16}}{3},0} \right)$

Normal $:y - 2 =  - \frac{5}{3}\left( {x - 2} \right) \Rightarrow R\left( {\frac{4}{5},0} \right)$

Area is $ = \frac{1}{2}\left( {QR} \right) \times 2 = \frac{{68}}{{15}}$

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