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The equation of circle which passes through (1,0),(0,1) & has its Radius as smal as possible is?
 one year ago
 one year ago
The equation of circle which passes through (1,0),(0,1) & has its Radius as smal as possible is?
 one year ago
 one year ago

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ParthKohliBest ResponseYou've already chosen the best response.0
There's only one unique circle passing through (1,0) and (0,1) right?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
Thanks for clearing my doubts. That's what I was trying out
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
May I have a counterexample BTW?
 one year ago

rajathsbhatBest ResponseYou've already chosen the best response.3
dw:1357382125336:dw
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
Two circles that intersect, right. =)
 one year ago

rajathsbhatBest ResponseYou've already chosen the best response.3
the smallest circle is the one that has the line connecting the two points as the diameter.
 one year ago

DLSBest ResponseYou've already chosen the best response.1
and why are there 2 circles
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
Radius of \(1\)? dw:1357382192536:dw
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
That's just the unit circle.
 one year ago

rajathsbhatBest ResponseYou've already chosen the best response.3
all other circles have this line as their chord which means that their diameters are longer that this line. An extreme example:dw:1357382299966:dw
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
If you draw a line segment, you'd get a segment with length \(\sqrt 2\). That is the smallest segment (and the only) possible. Now you get a triangle. Draw a circle around that triangle and that would be \(x^2 + y^2 = 1\).dw:1357382531256:dw
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
\[r^2 = h^2 + (k  1)^2 = (h  1)^2 + k^2\]
 one year ago

DLSBest ResponseYou've already chosen the best response.1
I just want to know why should they be diameterically opp..to satisfy the eq.nothing else :/
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
\[h^2 + k^2 2k+1=h^2  2h + 1 + k^2\]\[2h + 1 = 2k +1 \iff h =k\]So \((0,0)\)?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
\((0,0)\) is the center.
 one year ago

DLSBest ResponseYou've already chosen the best response.1
why u no tell jitna pucha :(
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
Pakka yahi hai answer.
 one year ago

rajathsbhatBest ResponseYou've already chosen the best response.3
the concept is pretty straightforward. Look at this diagramdw:1357382709667:dw The line you see is the line connecting (1,0) and (0,1) And i've drawn two circles that pass though the two points. The line drawn is a chord for the bigger circle which means that it's diameter is bigger that the line, ok? But look at the other circle which has the line as the diameter. It's obviously smalller than the other circle but also smaller than any other circle that can be drawn though those two points (again because chords are smaller than diameters)dw:1357383015575:dw So, the circle you're looking for is the circle that has that line for it's diameter. Simple.
 one year ago

DLSBest ResponseYou've already chosen the best response.1
not so clear but yeah somewhat..
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
another way to think is that you're looking for the smallest right triangle \(ABC\) where \(\angle B\) is the right angle as well as the center of the circle and the circle passes through \(A\) and \(C\).
 one year ago

DLSBest ResponseYou've already chosen the best response.1
how can (1,0) and (0,1) be diameterically opp but :O
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
I didn't say they were diametrically opposite =/
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
They are diametrically perpendicular...
 one year ago

rajathsbhatBest ResponseYou've already chosen the best response.3
No parth. I don't even know what that means... But i'll draw on paper and show you what I mean.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
dw:1357383885601:dw
 one year ago

DLSBest ResponseYou've already chosen the best response.1
kya yaa dimaag ka dahi mat karo :P aur bhi q hai!!
 one year ago

rajathsbhatBest ResponseYou've already chosen the best response.3
that's absolutely wrong. I can draw a smaller circle!dw:1357384070442:dw you see the point!? this right here the smallest circle.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
Oh, never thought of that =P
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
So then it's\[(x  0.5)^2 + (y  0.5)^2 = 0.25\]?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
So that's the trick. You make them diametrically opposite
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
@rajathsbhat Yaar chaa gaye =P
 one year ago

DLSBest ResponseYou've already chosen the best response.1
(xx1)(xx2)+(yy1)(yy2)=0 hoti hai equation diameterically op points ki :D
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
But we want the equation of the circle!
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
Achcha okay! Point noted
 one year ago
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