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sesenic [268]
3 years ago
11

In the diagram below,AB is the diameter of the circle with centre P.Point C lies on the y-axis.Given the coordinates of A and B

are (-6,3) and (2,-3) respectively ,calculate
a)the coordinates of P





b)radius of the circle





c)the coordinates of C





d)the area of the circle in term of
\pi
​

Mathematics
1 answer:
Step2247 [10]3 years ago
4 0

Answer:

<em>The coordinates of P are (-2,0)</em>

<em>The radius of the circle is 5.</em>

Step-by-step explanation:

<u>Analytic geometry</u>

The diagram shows a circle with center P, and two points A(-6,3) and B(2,-3) that form the diameter of the circle.

a)

The center of the circle lies at the midpoint of A and B. The midpoint (xm,ym) can be calculated by:

\displaystyle x_m=\frac{x_1+x_2}{2}

\displaystyle y_m=\frac{y_1+y_2}{2}

Substituting x1=-6, x2=2, y1=3, y2=-3:

\displaystyle x_m=\frac{-6+2}{2}=\frac{-4}{2}=-2

\displaystyle y_m=\frac{3-3}{2}=0

Thus, the coordinates of P are (-2,0)

b) The radius of the circle is the distance from the center to any point in its circumference. We can use the distance from P to A or B indistinctly.

Given two points A(x1,y1) and P(x2,y2), the distance between them is:

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

Substituting x1=-6, x2=-2, y1=3, y2=0:

r=\sqrt{(-2+6)^2+(0-3)^2}

r=\sqrt{4^2+(-3)^2}

r=\sqrt{16+9}=\sqrt{25}=5

The radius of the circle is 5.

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