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  • The radius of the circle which touches the circle <img alt="\mathrm{x^2+y^2-6 x+6 y +17=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E2&plus;y%5E2-6%20x&plus;6%20

The radius of the circle which touches the circle \mathrm{x^2+y^2-6 x+6 y +17=0} externally and to which the lines \mathrm{x^2-3 x y-3 x+9 y=0} are normals is __________.

Option: 1

4


Option: 2

2


Option: 3

3


Option: 4

0


Answers (1)

The given normals are \mathrm{x-3 y=0, x-3=0} which intersect at centre whose co-ordinates are (3,1). The given circle is \mathrm{C_1(3,-3), r_1=1, C_2\, \, is \, \, (3,1)\, \, and \, \, r_2=(?)}. If the two circles touch externally, then

\mathrm{ \begin{aligned} & C_1 C_2=r_1+r_2 \\ \therefore \quad & 4=1+r_2 \quad \therefore \quad r_2=3 . \end{aligned} }

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Ramraj Saini

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