Find all the intersection points of the following two circles:- The center circle (0,0) And its radius 13- The center circle (1, -1) And its radius 17(Note: Write the answer as follows (x1,y1)(x2,y2))

Question

Find all the intersection points of the following two circles:- The center circle (0,0) And its radius 13​- The center circle (1, -1) And its radius 17​(Note: Write the answer as follows (x1,y1)(x2​,y2​))

Clay Giles · Accepted Answer

Let the equation of circle is(x−h)2+(y−k)2=r2Where, h and k are the x and y coordinates of the center of the circle.And r is the radius of the circle.Find the equation of circles by given information,(x−0)2+(y−0)2=(13)2x2+y2=13x2+y2−13=0 (1)(x−1)2+(y−(−1))2=(17)2(x−1)2+(y+1)2=17x2+1−2x+y2+1+2y=17x2+1−2x+y2+1+2y−17=0 (2)Multiply equation (1) by -1 and add both the equation:−x2−y2+13=0After adding:1−2x+1+2y−4=0−2x+2y−2=0−x+y−1=0y=x+1Substitute the value of y in equation (1),x2+y2−13=0x2+(x+1)2−13=0x2+x2+1+2x−13=02x2+2x−12=0x2+x−6=0x2+3x−2x−6=0x2+3x−2x−6=0x(x+3)−2(x+3)=0(x+3)(x−2)=0x=−3,2x1=−3,x2=2y1=−3+1y1=−2y2=2+1y2=3

Find all the intersection points of the following two circles: -

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