Question

Does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?​
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Answer 1

Inside

Explanation:

Check the picture below

Answer 2

Given equation of the Circle is ,

`\sf\implies x^2 + y^2 = 25`

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 ,

`\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2`

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

`\sf\implies Distance = √( (0+4)^2+(2-0)^2) \\\\\sf\implies Distance = √( 16 + 4 ) \\\\\sf\implies Distance =√(20)\\\\\sf\implies\red{ Distance = 4.47 }`

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

Hence the point lies within the circle.