let us see if we can face some problems and if you can crack them immediately so are we ready with pen and paper ok let us go ahead. see the first question first question say is find the center and radius of each of the following Circles the first one is ready for us first is x square + y square equals  25 immediately everyone must have realized that this is type one, that is a standard Circle so if it is a standard circle we start off with comparison first has to be comparison, comparing the given equation with x square + y square equals a square what will get a square is equal to 25 perfect if a square is 25 I can say that means a will be 5. A, a was what right it was a radius so I got radius of the circle as five if the radius is 5 and if it is a standard circle I can immediately say the center of the circle is going to be( 0, 0) whereas the radius of the circle will be five is it very interesting and simple ok let us see the next one the next says is (X – 5 ) square +( y – 3)  square equals  20 very nice everyone must have identified that this is that type two question if it is that type 2 again I’ll compare the equation given equation with our type 2 formula that is centered radius form so when I compared with center radius form on left hand side just observe there is (X – H )square if it is (X – H )square I can say H is five and we can say case three alright so H is 5 case three did you observe right hand side, right hand side gives r square is equal to 20 right so much will be R perfect  R  is going to be square root of 20 as simple as that so i can say a directly the center of this circle that is h , k is( five , three) where r is the radius of the circle is square root of 20 if i calculate a  square root of 20 is nothing but 2 root 5 question 2 says find the equation of a circle with Center at origin and radius is 5 repeat find the equation of a circle with Center at origin center at origin center at the origin yes it is a type 1 type one problem as it is a standard circle if center-right origin we see it is a standard you remember that yes so if center of the circle is that origin and radius is a we have studied the equation is given by ( x square + y square) equals to a square very nice what is a there radius right I’ll be given radius ,yes radius is 4 so i can say here a value its 4 , so when i substitute a equation of the required circle will become x square + y square equals to a square that is 16.