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rectangular cartensian co-ordinates — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSrectangular cartensian co-ordinates1 Mark
MCQ
$A$ line segment $AB$ of length $\lambda$ moves such that the points $A$ and $B$ remain on the periphery of a circle of radius $\lambda$. Then the locus of the point, that divides the line segment $A B$ in the ratio $2: 3$, is a circle of radius
  • A
    $\frac{3}{5} \lambda$
  • B
    $\frac{\sqrt{19}}{7} \lambda$
  • C
    $\frac{2}{3} \lambda$
  • ✓
    $\frac{\sqrt{19}}{5} \lambda$
✓

Answer

Correct option: D.
$\frac{\sqrt{19}}{5} \lambda$
d
$h=\frac{\frac{2 \lambda}{\sqrt{2} \sin \theta}+3 \times \frac{\lambda}{\sqrt{2}} \cos \theta}{5}$

$k=\frac{\frac{-2 \lambda}{\sqrt{2}} 2 \cos \theta+\frac{3 \lambda}{\sqrt{2}} \sin \theta}{5}$

$h^2+k^2=\frac{19 \lambda^2}{5}$

$r=\frac{\sqrt{19} \lambda}{5}$

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