circles

find the eq. to the circle which touches the x-axis , passes through the pt.(1,1)&whose centre lies in the first quadrant on the line x+y=3 .

1 Answers

See,

Since the center lies on x+y=3, take any parametric point on it as (t,3-t) as the center.

Hence equation of circle is (x-t)²+(y-3+t)² = (3-t)² (Since the circle touches the x axis => y cordinate of center = Radius)

Now it passes through (1,1). Put it in above and get the values of t for which the circle lies in I^st Quadrant.

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