Kindly explain this whole topic clearly and give two new examples make it clear

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3:42 PM 8.1 K/s 25 DATE NO Equation of a circle centered at (0, 0 ) In the standard form of equation of a circle . ( x - h ) 2 + ( y - k ) 2 - r , if hoo and k. O, then atyarn. Example 1 Write the equation of a circles in standard form with radius 3 and center at (0, 0 ) Solution Using the equation x 2 ty2. r? and 1: 3, * fun . 32 Example 2 write the equation of a circle in standard form with radius s and center at (0 0 ) Solution : since the circle is centered at the origin and r'S the standard equation of the and is : * " ty . s 1= 25 NEC O D3:42 PM 8.1 K/s 25 DATE NO 9:14-21 GENERAL FORM OF A CIRCLE A + 2 1 Au2 + DX + By 1 F - 0 , where At O STANDARD FORM OF A CIRCLE ( x - h ) ? f ( 4 - k ) 2 =,2 Example : 1 Determine the general equation of a circle whose center is (3 , -1 ) and whose graph contains the point ( 7 , -1 ). sketch the graph 2 Find the general equation of the circle whose center is ( 2 , 6 ) and whose r = 3 . PROBLEM SOLVING AND APPLICATIONS Example Find the standard equation of the circle whose diameter has endpoints ( - S , 3 ) and ( 1 , 1 1 ) Example 1 : VEDO Screenshot has been saved to Pictures/ Screenshot O D3:42 PM 8.1 K/s 25 DATE NO 2. Find the general equation of the circle whose center is ( 1, 6 ) and whose r= 3 6 . ( 2 , G ) In center ( 2, Le) F6 Solution : 12 = ( x - h ) 2 + ( y -k ) 2 ( 2 . ( * - 2 ) 2 + ( y - 6 ) 3 = X * 2 - 4 * +4 + 42 - 124 + 36 9 - * 2 - 4 x +4 +92- my + 36 9 = x - * 2 - 4 * + 42 - 124 + 40 - 40+9 = x2+ 42- 4x- my x2+ 92- 4x - 124GB1 = 0 ... V O D3:42 PM 5.9 K/s 25 DATE NO 12 . ( x2 - x , ) " + ( y 2 - 4 1 ) 2 r 2 . ( 7 - 3 ) 2 + ( 1 71 ) 2 r2- 16 1 3 1 16 * 4 42 . ( x - B ) 2 + ( 4 + 1 ) 2 1 6 = x 2 - 6 * + 9 + 9 2 + 2 9 -+ 1 16 0 x 2 - 6 x + 4 2 + 24 + 10 -10 + 16 . x 2 + 4 2 - 6 * + 2y 6 . x 2 + 4 2 - 6 * + 2y x 2 + 92 - 4 x + 24 - 6 = 0 Screenshot has been saved to Pictures/ Screenshot O