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Two chords are drawn from the point P(h, k) on the circle x^2+y^2=h x+k y. If the y-axis divides both the chords in the ratio 2:3, then
 

Option: 1

k^2>15 h^2


Option: 2

15 k^2>h^2


Option: 3

h^2=15 k^2


Option: 4

None of these.


Answers (1)

best_answer

Point P(h, k) is lying on the circle. Let the y-axis divides the chords in the ratio 2:3 at the point (0, \beta). Then co-ordinates of the other end of the chord will be \left(-\frac{3 h}{2}, \frac{5 \beta-3 k}{2}\right). This point will lie on the circle.
\Rightarrow for two distinct values of \beta, 64 k^2-60\left(h^2+k^2\right)>0
\Rightarrow 4 \mathrm{k}^2>60 \mathrm{~h}^2 \Rightarrow \mathrm{k}^2>15 \mathrm{~h}^2 \text {. }

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Nehul

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