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  • If a circle S(x, y)=0 has tangent x+y=5 at the point (2,3) and S(1,2)=0, then find the radius of the circle.Option: 1 <img alt="\frac{1}{4}" src="htt

If a circle S(x, y)=0 has tangent x+y=5 at the point (2,3) and S(1,2)=0, then find the radius of the circle.

Option: 1

\frac{1}{4}


Option: 2

\frac{1}{\sqrt{3}}


Option: 3

\frac{1}{2}


Option: 4

\frac{1}{\sqrt{2}}


Answers (1)

best_answer

Equation of family of circles touching line x + y – 5= 0 at (2, 3) is \mathrm{(x-2)^2+(y-3)^2+\lambda(x+y-5)=0} Also, (1, 2) lies on it.

\mathrm{\begin{aligned} & \therefore 1+1+\lambda(-2)=0 \Rightarrow \lambda=1 \\ & \Rightarrow x^2+y^2-3 x-5 y+8=0 \end{aligned}}

\mathrm{\Rightarrow \text { Radius }=\frac{1}{\sqrt{2}} \text { units. }}

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Gaurav

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