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  • Points P(–3,2),Q(9,10) and (a,4) lie on a circle C with PR as its diameter, The tangents to C at the points Q and R intersect at the point S. If S lies on the line 2x – ky = 1, then k i

Points P(–3,2),Q(9,10) and (a,4) lie on a circle C with PR as its diameter, The tangents to C at the points Q and R intersect at the point S. If S lies on the line 2x – ky = 1, then k is equal to

Option: 1

3


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Equation of circle is

(x+3)(x-\alpha)+(y-2)(y-4)=0

Q lies on it

$$ \begin{aligned} & 12(9-\alpha)+8 \times 6=0 \\ & \alpha=13 \end{aligned}
$$ x^2+y^2-10 x-6 y-31=0
Equation of Tangent at \mathrm{Q}
$$ \begin{aligned} & x .9+y .10-5(x+9)-3(y+10)-31=0 \\ & 4 x+7 y=106 \, \, \, \, \, \, \, ...(1)\\ & \end{aligned}
Equation of Tangent at \mathrm{R}
$$ \begin{aligned} & x .13+y .4-5(x+13)-3(y+4)-31=0 \\ & 8 x+y=108 \, \, \, \, \, \, \, \, \, .....(2)\\ & \end{aligned}
Solution (1) and (2)
$$ \mathrm{s}=\left(\frac{25}{2}, 8\right)
which lies on 2 x-k y=1
$$ \mathrm{k}=3

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