E.g., $A(0,2)$ lies on Circle $C$: $x^2+y^2+3x+4y-12=0$. Line $L$ passes through $A$ and divides the circle into two equal halves. Find the equation of $L$.
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2What have you tried? Have you drawn a diagram? Please show some of your thoughts here and more people will be willing to help you out – lioness99a Mar 02 '20 at 09:42
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This site may help you find the opposite point on the circle, after which the question should be trivial – lioness99a Mar 02 '20 at 09:51
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Do you know how to find the coordinates of the center of $C$ from its equation? – J. W. Tanner Mar 02 '20 at 10:22
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Complete the squares to find a form of the equation for the circle $C$
from which it is easy to find the coordinates of its center:
$\left(x+\frac32\right)^2+(y+2)^2=r^2$.
Now you have two points on line $L$.
Can you take it from here?
J. W. Tanner
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