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allsm [11]
2 years ago
5

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

Mathematics
2 answers:
Len [333]2 years ago
5 0

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 = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{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 .

Anna11 [10]2 years ago
4 0

inside the circle

Step-by-step explanation:

we want to verify whether (-4,2) lies inside or outside or on the circle to do so recall that,

  1. if \displaystyle (x-h)^2+(y-k)^2>r^2 then the given point lies outside the circle
  2. if \displaystyle (x-h)^2+(y-k)^2 then the given point lies inside the circle
  3. if \displaystyle (x-h)^2+(y-k)^2=r^2 then the given point lies on the circle

step-1: define h,k and r

the equation of circle given by

\displaystyle  {(x - h)}^{2}  + (y - k) ^2=  {r}^{2}

therefore from the question we obtain:

  • \displaystyle  h= 0
  • \displaystyle  k= 0
  • {r}^{2}  = 25

step-2: verify

In this case we can consider the second formula

the given points (-4,2) means that x is -4 and y is 2 and we have already figured out h,k and r² therefore just substitute the value of x,y,h,k and r² to the second formula

\displaystyle  {( - 4  - 0)}^{2}  + (2 - 0 {)}^{2} \stackrel {?}{ < }  25

simplify parentheses:

\displaystyle  {( - 4 )}^{2}  + (2  {)}^{2} \stackrel {?}{ < }  25

simplify square:

\displaystyle  16 + 4\stackrel {?}{ < }  25

simplify addition:

\displaystyle  20\stackrel { \checkmark}{ < }  25

hence,

the point (-4, 2) lies inside the circle

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