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

Question

does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?​
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King 3 years 2021-08-02T10:55:27+00:00 2 Answers 20 views 0

Answers ( )

  1. Sapo1
    0
    2021-08-02T10:56:33+00:00
    Reply

    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

    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

  2. dangkhoa
    0
    2021-08-02T10:57:14+00:00
    Reply

    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 .

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )