Circle - analytics geometry

Write the equation of the circle that passes through the points Q[3.5] R[2.6] and has its center on the line 2x+3y-4=0.

Correct answer:

e : (x+1)^2+(y-2)^2=25

Step-by-step explanation:

Q=(3,5) R=(2,6)  p: 2x+3y−4=0 p: y = (4−2x)/3  S=(x0​,y0​)  ∣SQ∣=∣SR∣=r ∣SQ∣2=∣SR∣2=r2  (x−Qx​)2+((4−2⋅ x)/3−Qy​)2=(x−Rx​)2+((4−2⋅ x)/3−Ry​)2 (x−3)2+((4−2⋅ x)/3−5)2=(x−2)2+((4−2⋅ x)/3−6)2  10x=−10  x=10−10​=−1  x=−1  x0​=x=(−1)=−1 y0​=(4−2⋅ x)/3=(4−2⋅ (−1))/3=2  S=(−1,2) r=(x0​−Qx​)2+(y0​−Qy​)2​=((−1)−3)2+(2−5)2​=5  e: (x−x0​)2+(y−y0​)2=r2  e:(x+1)2+(y−2)2=25

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