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Find the equations of the circles which touch both the axis and pass through the point (2,1)?

Find the equations of the circles which touch both the axis and pass through the point (2,1)?
 

Grade:11

2 Answers

Arun
25763 Points
3 years ago
 

general equation of circle is

 

(x-h)2 + (y-k)2 = R2

 

when circle touches both the axis then h = k = R

 

(x-h)2 + (y-h)2 = h2

 

now this circle passes through (3,-6) so

 

(2-h)2 + (1-h)2 = h2

 

 h2 - 5h + 5 = 0

 

 Find h and put it in the equation of circle.

 

 

Regards

Arun (askIITians forum expert)

Ankit
29 Points
3 years ago
The circle which touches the both the coordinates have x and y coordinate of centre equal to its radius so it`s centre is (r,r) and radius is also r . Now eqn. of circle is (x-r)^2 + (y-r)^2 =r^2 . Solving we get x^2 +y^2 -2rx-2ry +r^2 . Now (2,1) lies on the circle so on putting value of x and y we get 2 values of r that are 2,3 . Now use these values to get circles on putting these values we get two circles . Thanks

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