The line PQ is the diameter of a circle, where points P and Q have the coordinates (4,7) and (-8,3) respectively. Find the equation of the circle.
Start by using the formula d = sqrt((x2-x1)2+(y2-y1)2)Therefore, substituting in our coordinates from P and Q:Length PQ = sqrt((-8-4)2+(3-7)2)= sqrt((-12)2+(-4)2)= sqrt(160)= sqrt(16) x sqrt(10)= 4 sqrt(10).This is our value of the diameter, so we halve to get the radius.r = 2sqrt(10)The centre is found at the coordinates ((x1+x2)/2, (y1+y2)/2),Using our coordinates at P and Q again,the centre is ((4+(-8))/2, (7+3)/2), simplified to (-2, 5)The default equation of the circle where the centre is not at the origin takes the form (x-a)2+(y-b)2=r2, where a and b are the x and y coordinates for the centre of the circle and r is the radius. Now we simply plug these values from before in.(x+2)2+(y-5)2=4 sqrt(10)2Simplify to get:(x+2)2+(y-5)2= 40
