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JulsSmile [24]
3 years ago
9

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

Mathematics
2 answers:
Ber [7]3 years ago
8 0

Answer:

inside the circle

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 25 ← is in this form

with r = \sqrt{25 = 5

Calculate the distance d from the centre to the point (- 4, 2 ) using the distance formula

d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2    }

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 4, 2)

d= \sqrt{(-4-0)^2+(2-0)^2}

   = \sqrt{(-4)^2+2^2}

   = \sqrt{16+4}

    = \sqrt{20}

    ≈ 4.5 ( to 1 dec. place )

Since 4.5 is less than the radius of 5

Then (- 4, 2 ) lies inside the circle

stiv31 [10]3 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 ,

• <u>Radius</u> = 5 units

• <u>Centre </u> = (0,0)

<u>Finding</u><u> </u><u>distance</u><u> between</u><u> </u><u>the </u><u>two </u><u>points</u><u> </u><u>:</u><u>-</u><u> </u>

\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.

<u>Hence </u><u>the</u><u> </u><u>point</u><u> </u><u>lies </u><u>within</u><u> </u><u>the </u><u>circle</u><u> </u><u>.</u>

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