$\begin {array} {1 1} (A)\;\text{ lies inside the circle} & \quad (B)\;\text{ lies outside the circle} \\ (C)\;\text{ lies on the circle} & \quad (D)\;\text{ none of the above} \end {array}$

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- If the distance between the point through which the circle passes say $(x_1, y_1)$ is less than the radius, then the point lies inside the circle.
- If it is greater then it lies outside the circle.
- If it is equal, then it lies on the circle.

Step 1 :

The equation of the given circle is $x^2+y^2=25$

This can be written as

$(x-0)^2+(y-0)^2=5^2$-------(1)

which is of the form

$(x-h)^2+(y-k)^2=r^2$--------(2)

Comparing both the equations we get,

$h=0, r=0$ and $ r=5$

Hence the centre is (0,0) and radius = 5.

$ \therefore$ The distance between the point (-2.5, 3.5) and centre (0,0) is

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

$ = \sqrt{6.25+12.25}$

$ = \sqrt{18.5}$

$ = 4.3

This distance is lesser than 5

That is less than the radius

Hence the point lies inside the circle.

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