Determine 82394

Determine the equation of the circle that passes through the point M(-1,2) and N( 3,0) and whose center lies on the line p: x=-3+t, y=-1+t,

Correct answer:

e : (x-3)^2+(y-5)^2=25

Step-by-step explanation:

M=(−1,2) N=(3,0)  p: x=−3+t, y=−1+t  S=(x0​,y0​)  ∣SN∣=∣SM∣=r ∣SN∣2=∣SM∣2=r2  ((−3+t)−Mx​)2+((−1+t)−My​)2=((−3+t)−Nx​)2+((−1+t)−Ny​)2 ((−3+t)−(−1))2+((−1+t)−2)2=((−3+t)−3)2+((−1+t)−0)2  4t=24  t=424​=6  t=6  x0​=−3+t=−3+6=3 y0​=−1+t=−1+6=5  r=(x0​−Mx​)2+(y0​−My​)2​=(3−(−1))2+(5−2)2​=5  e: (x−x0​)2+(y−y0​)2=r2  e:(x−3)2+(y−5)2=25

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