Write an equation of a circle with center {-1,2} passing through the point {2,4}

The equation of circle passing through points  (2, 4) and center (-1 , 2) is (x  + 1 )² + (y - 2)² = 13

Step-by-step explanation:

Given as :

The circle having center = (-1 , 2)

The circle passes through point = (2, 4)

Now, Standard equation of circle with center and passing through points is

(x - h)² + (y -k)² = r²

where h and k are the center of circle and r is the radius of circle

Now the center as (h,k) = (-1 , 2)

And passing through points (x,y) = (2, 4)

Now, satisfying the center and points on standard circle equation

I.e (x - h)² + (y -k)² = r²

Or, (2 - (-1) )²+ (4 -2)² = r²

or, 3² + 2² = r²

or,  r² = 9 + 4

Or ,  r² = 13

∴  r =

Now circle equation

(x - (-1) )² + (y -2)² = ()²

or, (x  + 1 )² + (y - 2)² = 13

So, equation of circle is (x  + 1 )² + (y - 2)² = 13

Hence The equation of circle passing through points  (2, 4) and center        (-1 , 2) is (x  + 1 )² + (y - 2)² = 13   Answer

step-by-step explanation:

given perimeter: 28cm

length: 9cm

atp,

2(l+w)=p of the reactangle

2(9+x)=28

18+2x=28

2x=28-18

x=10/2

x=5

therefore width is 5 cm

$12. that is my answer.