If y = mx + 10 is the tangent to the circle x2 + y2 = 5 then find the value of m ?

Question

Question

Answer 1

CONCEPT:

If the line y = mx + c is a tangent to the circle x2 + y2 = a2 then c2 = a2 (1 + m2)

CALCULATION:

Given: Equation of line is y = y = mx + 10 and the line is tangent to the circle x2 + y2 = 5

Here, we have to find the value of m.

As we know that, if the line y = mx + c is a tangent to the circle x2 + y2 = a2 then c2 = a2 (1 + m2)

By comparing the given equation of line and circle with y = mx + c and x2 + y2 = a2 respectively, we get

⇒ c = 10 and a2 = 5

⇒ c2 = 100

∵ c2 = a2 (1 + m2)

By substituting a2 = 4 and c2 = 256 in the above equation we get,

⇒ 100 = 5 ⋅ (1 + m2)

⇒ 1 + m2 = 20

⇒ m = ± √19

Hence, option B is the correct answer.