Question

e) Find the equation of the circle through the points (4,3) and (-2,5) and having its centre on the line
2x  3y  4

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Answer 1

Answer: (x+1)2+(y+2)2=50

step by step :Let  C(x,y)  be center of circle

Then  C  is equidistant to points  (4,3)  and  (−2,5)  

(x−4)2+(y−3)2=(x+2)2+(y−5)2x2−8x+16+y2−6y+9=x2+4x+4+y2−10y+25−12x+4y=4−3x+y=1y=3x+1  

Since  C  is also on the line  2x−3y=4 , then:

2x−3(3x+1)=42x−9x−3=4−7x=7x=−1y=−2  

r2=(−1−4)2+(−2−3)2=25+25=50