For which value of k the following pair of equations give a unique solution for x such that solution is posit?

Question

For which value of k does the following pair of equations give a unique solution for x such that solution is positive
x^2-y^2=0
(x-k)^2 + y^2=1
(a) 2
(b) 0
(c) square root of 2
(d) -square root of 2

Answer 1

(c)

first equation represent pair of lines, where as second equation is a circle with (k,0) as centre and radius 1.

draw graph, and solve graphically

Answer 2

well if you solve for X in the first equation you get
X=Y
substitute X for Y in the second equation and you have:
(X - k)^2 + X^2 = 1
then plug in your available answers to find such X value.

Answer 3

x²-y²=0 ==> x²=y² ==> x = y and x = -y so the limitations on the answer are {x,-x} considering (x-ok)²+y² = a million describes a circle with radius a million based at x = ok on the x axis, it really is fairly obvious (through inspection) that -?2 and 0 are out. If ok = ?2, then there is not any unique answer so it may be that ok = 2. Doug

Answer 4

2X^2-2kX+k^2-1=0 solve this then you can find ans