What is the length of the tangent to the circle x2 + y2 = 9 from the point (4, 0).

  1. √7 units
  2. √6 units
  3. √11 units
  4. √17 units

Answer (Detailed Solution Below)

Option 1 : √7 units
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Concept:

The length of the tangent from an external point (x1, y1) to the circle x2 + y2 = a2 is \(\sqrt {x_1^2 + y_1^2 - {a^2}}\)

Calculation:

Given: Equation of circle x2 + y2 = 9 and the point (4, 0).

As we know that, the length of the tangent from an external point (x1, y1) to the circle x2 + y2 = a2 is \(\sqrt {x_1^2 + y_1^2 - {a^2}}\)

Here, x1 = 4 , y1 = 0 and a2 = 9.

So, the length of the tangent is √7 units.
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