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Question 2 : The shortest distance from the point (-4,3) to the circle x^{2} + y^{2} = 1 is __________.

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From the above diagram, we can see that, we can draw many lines to the circle that can be a secant or a tangent. We need to find the line which gives us the shortest distance of the point from the circle.

It is very evident that the line joining the center of the cirle to the point (-4,3) will give us the shortest distance.

As we can see from the diagram, we have a right triangle with base length as 4 and height as 3. Therefore the distance of the point (-4,3) from the center of the circle is the hypotenuse and its length is 5. (3,4,5 is a pythagorean triplet)

Therefore, the distance of the point (-4,3) from the circle = 5 - radius of the circle = 5 - 1 = 4

The question is **" The shortest distance from the point (-4,3) to the circle x ^{2} + y^{2} = 1 is __________. " **

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