Respuesta :
Answer:
The equation of the circle is given by,
[tex](x-2)^{2} + (y-4)^{2} = (\sqrt{13})^{2}[/tex]
Step-by-step explanation:
The center of the circle is given as (-1,2) and it passes through (2,4).
The distance between the two points is radius of the circle.
[tex](Distance) = \sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]
Radius = [tex]\sqrt{(2-(-1))^{2}+(4-2)^{2}}[/tex]
Radius = [tex]\sqrt{13}[/tex]
The equation of the circle is given by,
[tex](x-x1)^{2} + (y-y1)^{2} = (Radius)^{2}[/tex]
Inserting above values,
[tex](x-2)^{2} + (y-4)^{2} = (\sqrt{13})^{2}[/tex]
Answer:
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 = [tex]\sqrt{13}[/tex]
Now circle equation
(x - (-1) )² + (y -2)² = ([tex]\sqrt{13}[/tex])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
