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Find the center and the radius of the circle.
(x-4)^2 + (y + 3)^2 = 74

User Newbie
by
8.2k points

2 Answers

7 votes

Answer:

  • radius =
    √(74)
  • center =
    (4,-3)

Explanation:

We would like to calculate the centre and the radius of the circle . The given equation is ,


\longrightarrow (x - 4)^2+(y+3)^2=74

As we know that the Standard equation of circle is given by ,


\longrightarrow (x - h)^2+(y-k)^2=r^2

where ,


  • (x,y) is a point on circle .

  • (h,k) is the centre of circle .

  • r is the radius of the circle .

We can rewrite the equation as ,


\longrightarrow (x-4)^2+\{ y -(-3)\}^2=(√(74))^2\\

Now on comparing to the standard form , we have ;

  • radius =
    r =
    √(74)
  • center =
    (h,k) =
    (4,-3)

Graph :-


\setlength{\unitlength}{7mm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\circle*{0.2}}\put(0.2, - .1){(4,-3)}\put(-1.2,0){\vector(0,1){5}}\put(-1.2,0){\vector(0, - 1){5}}\put(-1,0.7){\vector(1,0){5}}\put(-1,0.7){\vector( - 1,0){5}}\put(0,0){\line(-1,0){2.3}}\put( - 1.2,-0.7){$\sf √(74)$}\put(2,6){$\boxed{\sf \textcopyright \: RISH4BH }$}\end{picture}

And we are done !

Find the center and the radius of the circle. (x-4)^2 + (y + 3)^2 = 74-example-1
User FatherMathew
by
8.1k points
8 votes

We are given the equation of circle (x - 4)² + (y + 3)² = 74 , but let's recall the standard equation of circle i.e (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r being the radius ;

So, consider the equation of circle ;


{:\implies \quad \sf (x-4)^(2)+(y+3)^(2)=74}

Can be further written as ;


{:\implies \quad \sf (x-4)^(2)+\{y-(-3)\}^(2)=({√(74)})^(2)}

On comparing this equation with the standard equation of Circle, we will get, centre and radius as follows

  • Centre = (4, -3)
  • Radius = √74 units
User Lopata
by
8.0k points

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