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The line x=y touches a circle at the point (1, 1) If the circle also passes through the point (1,-3)

Опубликовано: 21 Октябрь 2024
на канале: Math Master - Impetus Gurukul
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#circle #propertiesofcircle #systemofcircle
The line x=y touches a circle at the point (1, 1), If the circle also passes through the point (1,-3), then its radius is
(a) 2√2 (b) 3√2 (c) 3 (d) 2
Ans: a
Sol.
Equation of circle touching the line x=y at point (1, 1) is given by
(x-1)^2+(y-1)^2+λ(x-y)=0
Since it also passes through the point (1,-3)
∴0+(-3-1)^2+λ(1+3)=0⇒λ=-4
∴ From (i), (x-1)^2+(y-1)^2-4(x-y)=0
⇒x^2+1-2x+y^2+1-2y-4x+4y=0
⇒x^2+y^2-6x+2y+2=0
∴ Radius of the circle
=√(9+1-2)=2√2 units

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