find the equation of the concentric circle with the circle X*x+y*y-8x+6y-5=0 and passing through the point (-2,-7)
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What is the equation of the circle concentric with the circle x2+y2+6x−10y+33=0x2+y2+6x−10y+33=0and touching the line x=0?
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Pam Nicson, studied Mathematics & Physics at High School Students (2018)
Answered Jun 19 · Author has 155 answers and 41.3k answer views
x2+y2+6x−10y+33=0x2+y2+6x−10y+33=0
x2+6x+9+y2−10y+25+33=25+9x2+6x+9+y2−10y+25+33=25+9
(x+3)2+(y−5)2=1(x+3)2+(y−5)2=1
C(−3,5)C(−3,5) , r=1r=1 for first circle.
If the second circle is touching the x=0x=0 line, it means it touches 0,00,0 center of coordinate table.
For the second circle, the equation of it is the same: (x+3)2+(y−5)2−r2=0(x+3)2+(y−5)2−r2=0
As the circle touches 0,00,0 point, it means it does satisfy the equation.
So we substitute x=0x=0 and y=0y=0.
(0+3)2+(0−5)2−r2=0(0+3)2+(0−5)2−r2=0
9+25=r29+25=r2
r2=34r2=34.
As we find the radius, the equation would be:
(x+3)2+(y−5)2=34(x+3)2+(y−5)2=34
x2+6x+y2−10y=0x2+6x+y2−10y=0
Tell me if I am wrong. Some seemed to find 2525instead of 3434, but to be honest, I didn’t understand the way they taught how they found 2525.
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7 ANSWERS

Pam Nicson, studied Mathematics & Physics at High School Students (2018)
Answered Jun 19 · Author has 155 answers and 41.3k answer views
x2+y2+6x−10y+33=0x2+y2+6x−10y+33=0
x2+6x+9+y2−10y+25+33=25+9x2+6x+9+y2−10y+25+33=25+9
(x+3)2+(y−5)2=1(x+3)2+(y−5)2=1
C(−3,5)C(−3,5) , r=1r=1 for first circle.
If the second circle is touching the x=0x=0 line, it means it touches 0,00,0 center of coordinate table.
For the second circle, the equation of it is the same: (x+3)2+(y−5)2−r2=0(x+3)2+(y−5)2−r2=0
As the circle touches 0,00,0 point, it means it does satisfy the equation.
So we substitute x=0x=0 and y=0y=0.
(0+3)2+(0−5)2−r2=0(0+3)2+(0−5)2−r2=0
9+25=r29+25=r2
r2=34r2=34.
As we find the radius, the equation would be:
(x+3)2+(y−5)2=34(x+3)2+(y−5)2=34
x2+6x+y2−10y=0x2+6x+y2−10y=0
Tell me if I am wrong. Some seemed to find 2525instead of 3434, but to be honest, I didn’t understand the way they taught how they found 2525.
543 Views
Sponsored by UpGrad.com
Become an AI engineer with PG program from IIIT Bangalore.
360 degree career support, IIIT Bangalore alumni status and 1:1 mentorship.
Learn More
RELATED QUESTIONS (MORE ANSWERS BELOW)
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