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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: Circles-easy but ajeeb question
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tarinbansal (3898)

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2 circles x^2+y^2=6, x^2+y^2 - 6x +8=0 are given. Then the equation of the circle thru their point of intersection and the point (1,1) is-
 
Ans---> x^2+y^2 - 3x + 1=0
 
I called this ''ajeeb'' becoz, if you find the point of intersection of these 2 given circles by putting x^2+y^2=6 in the second equation, we get x= - +7/2. Now you keep this value in the equation x^2+y^2=6, you get y^2= -25/4 which is not possible. It means that their point of intersection does not exist. Then how come the answer came?
Please help
 
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akhileshsk (7)

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question is wrong because only oneline can be drawn thats the radical axis.(1,1) does not satisfy it check it out
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pardesi (541)

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clearly C_{1}:(0,0) r_{1}=root(6)
C_{2}:(3,0) r_{2}=1
C_{1}C_{2}=3 <1+ root(6) So the circles have  to  intersect at real points


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pardesi (541)

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(1,1) is a point inside the first circle and outside the second
why doesn't it satisfy the equation
for  1st it is 2 and for second also it is 2
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tarinbansal (3898)

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Abe yeh to theek hai ki circles have to intersect at real points but why I am not getting real points by solving the circles? How to do this question?

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pardesi (541)

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tarin please do mind ur language while typing come straight to the point no need of anointing
well u have done a silly mistake
putting x^2+y^2=6
 in the second equation gives
6-6x+8=0 this gives 14=6x so x=7/3 and not 7/2
rest everything is fine

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tarinbansal (3898)

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Hey pardesi,
yaar bura kyon maan gaye? I AM SORRY. Khush!
Thanx for solving the question. Here's ur 5 pointer.

The quality of a person's life is in direct proportion to their commitment to excellence, regardless of their chosen field of endeavor.

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pardesi (541)

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no probs
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akshay.khare91 (480)

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the answer is correct because if getting the negative value of y
then it means that it is intersecting in the coordinate where
y is negative ..... it doesnot means that circle donot intersect each other

I DONOT FOLLOW THE RULES I MAKE THEM TO FOLLOW ME.
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