if x^2 + y^2 =1 and (x-a)^2 + (y-b)^2 = 1, what is the value

Question

if x^2 + y^2 =1 and (x-a)^2 + (y-b)^2 = 1, what is the value of y ?

1) a=0 and b=2
2) a=1 and b=0

HIMALAYA · Answer

Frankly, i do not like this type of question because the information given for the variables a and b are contradictory. IMO in real test questions with such contradictory information are rare.

sparky · Answer

, ok, but it still can be solved, can't it? I just wanted to make it easier, eliminating C and E.

let's make it like this then

________________________________________________________
if x^2 + y^2 =1 and (x-a)^2 + (y-b)^2 = 1, what is the value of y ?

1) a = 0
2) 0< b < 2
________________________________________________________

maneeshkumar · Answer

This two are the eqation of Circle.

First one is a circle with center at (0,0) and radius as 1.
The Second eqation is of Circle with Center at (a,b) and radius as 1.

Now i guess by drawing figures it will be easy for all of you to solve this problem

In the firast case when a = 0 and b - 2 this gives centre of the second circle is at (0,2) so the common point of meeting or tanget point is (0,1) for both the Circles. 
This gives a unique answer y = 1.

Thus 1 qualifies.

Now lets Examine 2.

The centre of the second circle is (1,0)
As you can see from graph this will give two point of intersection so this cannot qualify as the answer.


Thus answer is A.

What is OA?

Folaa3 · Answer

A or D. I pick A because the answer from 2 alone is contradictory. 
What is the OA?

HowManyToGo · Answer

I vote for A.

The stem simply results in the equation.

a^2 + b^2 = 2x(a+b)

Now with 1) Y = 1 
with 2) Y = +/1 sqrt(3)/2

Hence A.

HMTG.

FN · Answer

The answer should be D

we have 2 equations, two unkowns...we can solve for both of them......

sparky · Answer

The original question, the answer is A

1) means circles touch at one point => y can be uniquely determined
2) circles cross, however crossing points have the same x coordinate but two different y coordinates => insufficient

maneeshkumar · Answer

Pl read the explanation above by my prevous post. Many times you do not go for solving equationa sit will take lof of time. If you know standard equztion of some of the common geometric figures then you cn draw a quick diagram and solve within 30 seconds and see what is the answer. Just in this case SPARY put up the question of two circles.

ashkg · Answer

Thanks man. I took quite some time to solve this and tried to get answers/values of Y by solving the equations which was actually not required if i had simply drawn the diagrams. This method really saves a lot of time

if x^2 + y^2 =1 and (x-a)^2 + (y-b)^2 = 1, what is the value

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