Answered

Discover new information and insights with the help of IDNLearn.com. Discover thorough and trustworthy answers from our community of knowledgeable professionals, tailored to meet your specific needs.

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

Sagot :

Answer:

Inside

Step-by-step explanation:

VirαtKσhliidn

Given equation of the Circle is ,

[tex]\sf\implies x^2 + y^2 = 25 [/tex]

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 ,

[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

[tex]\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 }[/tex]

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

Hence the point lies within the circle

Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. IDNLearn.com has the solutions you’re looking for. Thanks for visiting, and see you next time for more reliable information.