Given:

The equation of the given circle is x^{2} +y^{2} = 25.

x^{2} + y^{2} = 25

(x – 0)^{2} + (y – 0)^{2} = 5^{2}

[which is of the form (x – h)^{2 }+ (y – k)^{2} = r^{2}]

Where, h = 0, k = 0 and r = 5.

So the distance between point (-2.5, 3.5) and the centre (0,0) is

= \(\sqrt{(-2.5 – 0)^2 + (-3.5 – 0)^2}\)

= \( \sqrt{(6.25 + 12.25}\)

= \( \sqrt{18.5}\)

= 4.3 [which is < 5]

Since, the distance between point (-2.5, -3.5) and the centre (0, 0) of the circle is less than the radius of the circle, point (-2.5, -3.5) lies inside the circle.

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