Question

assignment 2.1
score: 4/5 4/5 answered
question 5
write the equation of the circle centered at (9,7) that passes through (3, - 3).

Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of a circle's equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius. Here, \(h = 9\), \(k = 7\).

Step2: Calculate the radius

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) to find the radius. Let \((x_1,y_1)=(9,7)\) and \((x_2,y_2)=(3,-3)\). Then \(r=\sqrt{(3 - 9)^2+(-3 - 7)^2}=\sqrt{(-6)^2+(-10)^2}=\sqrt{36 + 100}=\sqrt{136}\). So \(r^2 = 136\).

Step3: Substitute into the standard form

Substitute \(h = 9\), \(k = 7\), and \(r^2=136\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x - 9)^2+(y - 7)^2=136\).

Answer:

\((x - 9)^2+(y - 7)^2=136\)