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Given, a circle   As we can see center of the circle is ( 0,0) Now the distance between (0,0) and (–2.5, 3.5) is  Since distance between the given point and center of the circle is less than radius of the circle, the point lie inside the circle.
Let the equation of circle be : Now, since the centre of the circle is (2,2), our equation becomes Now, Since this passes through the point (4,5) Hence  The Final equation of the circle becomes
Let the equation of circle be, Now since this circle passes through (0,0) Now, this circle makes an intercept of a and b on the coordinate axes.it means circle passes through the point (a,0) and (0,b) So, Since  Similarly, Since b is not equal to zero. So Final equation of the Circle ;
As we know,  The equation of the circle with centre ( h, k) and radius r is given by ; So let the circle be, Since it's radius is 5 and its centre lies on x-axis, And Since it passes through the point  (2,3). When  ,The equation of the circle is : When  The equation of the circle is :
As we know,  The equation of the circle with centre ( h, k) and radius r is given by ; Given Here, Condition 1: the circle passes through points   (2,3) and (–1,1) Here,  Now, Condition 2: centre is on the line. From condition 1 and condition 2  Now let's substitute this value of h and k in condition 1 to find out  So now, the Final Equation of the circle is 
As we know,  The equation of the circle with centre ( h, k) and radius r is given by ; Given Here, Condition 1: the circle passes through  points (4,1) and (6,5) Here,  Now, Condition 2:centre is on the line . From condition 1 and condition 2  Now lets substitute this value of h and k in condition 1 to find out r  So now, the Final Equation of the circle is 
As we know,  The equation of the circle with centre ( h, k) and radius r is given by ; Given here  Can also be written in the form  So, from comparing, we can see that  Hence Center of the circle is the Radius of the circle is   .
As we know,  The equation of the circle with centre ( h, k) and radius r is given by ; Given here  Can also be written in the form  So, from comparing, we can see that  Hence the radius of the circle is .
As we know,  The equation of the circle with centre ( h, k) and radius r is given by ; Given here  Can also be written in the form  So, from comparing, we can see that  Hence the Radius of the circle is .
As we know,  The equation of the circle with centre ( h, k) and radius r is given by ; Given here  Can also be written in the form  So, from comparing, we can see that  Hence the Radius of the circle is 6.
As we know,  The equation of the circle with centre ( h, k) and radius r is given by ; So Given Here   AND  So the equation of the circle is: , 
As we know,  The equation of the circle with centre ( h, k) and radius r is given by ; So Given Here   AND  So the equation of the circle is: , 
As we know,  The equation of the circle with center ( h, k) and radius r is give by ; So Given Here   AND    So the equation of circle is: , 
As we know,  The equation of the circle with centre ( h, k) and radius r is given by ; So Given Here   AND  So the equation of the circle is: , 
As we know,  The equation of the circle with centre ( h, k) and radius r is given by ; So Given Here   AND  So the equation of the circle is: , 
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