# 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. RuslanHeatt

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 ,

• Centre = (0,0)

Finding distance between the two points :-

$$\begin{lgathered}\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }\end{lgathered}$$

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

Hence the point lies within the circle.

2. danthu

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 $$\displaystyle (x-h)^2+(y-k)^2<r^2$$ 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:

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

step2: 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:

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

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