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?​

in progress 0
Tài Đức 4 years 2021-08-02T07:43:07+00:00 2 Answers 13 views 0

Answers ( )

    0
    2021-08-02T07:44:17+00:00

    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.

    0
    2021-08-02T07:44:22+00:00

    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.

Leave an answer

Browse

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