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Grade 11Engineering Entrance Exams

Circle touching x-axis at a distance 3 from the origin and having an intercept of length 2root 7 on y-axis is ?

Profile image of Jayant Kumar
12 Years agoGrade 11
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2 Answers

Profile image of Saurabh Koranglekar
6 Years ago
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Profile image of Vikas TU
6 Years ago
Let equation of circle is ----
x^2+y^2+2gx+2fy+c=0========(2)
a/c to question,
circle touch x-axis at x=3
hence,
(3)^2+0+2(3)g+0+c=0
9+6g+c=0 -------------(1)
also we know circle touch x-axis then
g^2=c
put this above equation ,
9+6g+g^2=0
(g+3)^2=0
g=-3
again ,
put this equation (1)
9-18+c=0
c=9
a/c to question ,
y-intersept =6 unit
2√(f^2-c)=6
√(f^2-9)=3
aquaring both side
f=+_3√2
now put all constant in equation (2)
then ,
x^2+y^2-6x+(+_6√2)y +9=0
 

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