Which of the following lines is tangent to circle x^2 + y^2 = 8?

Question

(a) x + y = 2 
(b) x + y = 4 
(c) x + y = 6 
(d) x + y = 8 
(e) None of the above 

explain why please.

Answer 1

Step 1:

The circle equation is .

The line equations are , , and .

Let the tangent line equation be , where is a positive integer.

Substitute in to form a quadratic equation in .

.

Step 2:

Find the discriminant of the quadratic equation to obtain .

Since represents tangent line, .

Substitute and in .

.

Susbtitute in the line equation .

The tangent line equation to the curve is .

Solution :

The tangent line equation to the curve is .

Option (b) is correct.