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

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 ,

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.

Answer:The equation of the given circle is x

2

+y

2

=25

⇒ Centre =(0,0) and radius =5

Distance between point (−2.5,3.5) and centre (0,0)

=

(−2.5−0)

2

+(3.5−0)

2

=

6.25+12.25

=

18.5

=4.3(approx)<5

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

Hence the point (−2.5,3.5) lies inside the circle.