does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?​ ​

does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?​


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  1. Given equation of the Circle is ,

    [tex]\sf\implies x^2 + y^2 = 25 [/tex]

    And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

    [tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]

    Here we can say that ,

    • Radius = 5 units

    • Centre = (0,0)

    Finding distance between the two points :-

    [tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]

    Here we can see that the distance of point from centre is less than the radius.

    Hence the point lies within the circle.

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