Question

What is the equation of this circle in standard form?

Answer 1

I hope this helps you

Answer 2

Answer:

Standard equation of circle:

$(x-\frac{11}{2})^2+(y-4)^2=12.25$

Step-by-step explanation:

Given: Ends points of diameter are M(2,4) and N(9,4)

Mid point of M and N is center of circle.

Let center of circle be O(h,k)

Using mid point formula:

[tex[(x,y)\rightarrow (\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

$O(h,k)\rightarrow (\dfrac{2+9}{2},\dfrac{4+4}{2})$

$O(h,k)\rightarrow (\dfrac{11}{2},4)$

Distance between O and M is radius of circle.

Let radius of circle be r

Using distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

$r=\sqrt{(\dfrac{11}{2}-2)^2+(4-4)^2=3.5$

Standard equation of circle:

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

Equation of required circle:

$(x-\frac{11}{2})^2+(y-4)^2=3.5^2$

$(x-\frac{11}{2})^2+(y-4)^2=12.25$