manulath wrote:

Is line y=kx+b tangent to circle x^2+y^2=1 ?

(1) k+b=1

(2) k^2+b^2=1

OA:

Although the other solutions are mathematically correct, I think there's an easier way than memorizing a formula.

We need to solve for k and b.

1. A single equation does not allow us to solve for two variables. Additionally, k=1, b=0 gives an answer of no and k=0, b=1 gives an answer of yes. Insufficient.

2. See 1. Insufficient.

1+2. Taken together we have:

b=1-k

b^2=1-k^2

=> b^2=(1-k)^2=1-2k+k^2=1-k^2

==> 2k^2-2k=0 => k(2k-2)=0, and therefore k=0 or k=1.

In the case of k=0, b=1. Then the equation for the line is y=1, and the answer is YES. In the case of k=1, b=0. Then the equation for the line is y=x, and the answer is NO. Insufficient.

E.