The number of tangents that can be drawn from (2, 6) to x2 + y2 = 40 is

  1. 0
  2. 1
  3. 2
  4. more than 2

Answer (Detailed Solution Below)

Option 2 : 1
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Detailed Solution

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Concept:

If the point lies inside the circle no tangent can be drawn.

If the point lies on the circle then only one tangent can be drawn

If the point lies outside the circle then a maximum of two tangent lines can be drawn on the circle

Calculation:

Given point (2, 6) and equation of circle is x2 + y2 = 40

Now, x2 + y2 - 40 = 0

Put (2, 6) in this equation, we get

22 + 62 – 40 = 4 + 36 – 40 = 40 – 40 = 0

So, the point (2, 6) lies on the circle.

Hence, only one tangent can be drawn.

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