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Grade: 11
        
Find the equations of the circles which touch both the axis and pass through the point (2,1)?
 
6 months ago

Answers : (2)

Arun
12267 Points
							
 

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)

6 months ago
Ankit
29 Points
							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
						
6 months ago
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