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

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

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0Thanks for clearing my doubts. That's what I was trying out

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0May I have a counterexample BTW?

rajathsbhat
 3 years ago
Best ResponseYou've already chosen the best response.3dw:1357382125336:dw

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0Two circles that intersect, right. =)

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

DLS
 3 years ago
Best ResponseYou've already chosen the best response.1and why are there 2 circles

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0Radius of \(1\)? dw:1357382192536:dw

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0That's just the unit circle.

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

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0If 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

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0\[r^2 = h^2 + (k  1)^2 = (h  1)^2 + k^2\]

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

ParthKohli
 3 years ago
Best 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 \((0,0)\)?

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0\((0,0)\) is the center.

DLS
 3 years ago
Best ResponseYou've already chosen the best response.1why u no tell jitna pucha :(

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0Pakka yahi hai answer.

rajathsbhat
 3 years ago
Best ResponseYou've already chosen the best response.3the 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.

DLS
 3 years ago
Best ResponseYou've already chosen the best response.1not so clear but yeah somewhat..

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0another 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 \(C\).

DLS
 3 years ago
Best ResponseYou've already chosen the best response.1how can (1,0) and (0,1) be diameterically opp but :O

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0I didn't say they were diametrically opposite =/

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0They are diametrically perpendicular...

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

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1357383885601:dw

DLS
 3 years ago
Best ResponseYou've already chosen the best response.1kya yaa dimaag ka dahi mat karo :P aur bhi q hai!!

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

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0Oh, never thought of that =P

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

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0So that's the trick. You make them diametrically opposite

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0@rajathsbhat Yaar chaa gaye =P

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

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0But we want the equation of the circle!

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.0Achcha okay! Point noted
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