Question

Find the area of the circle passing through the points (-8,0), (0,8),12,0)

Answer 1

we have to find the area of circle passing through the points (-8,0), (0, 8) and (12, 0).

solution : general equation of circle is x² + y² + 2gx + 2fy + c = 0

putting (-8,0) in equation,

(-8)² + 0² + 2g(-8) + 2f(0) + c = 0

⇒64 - 16g + c = 0 ....(1)

putting (0,8) in equation,

(0)² + (8)² + 2g(0) + 2f(8) + c = 0

⇒64 + 16f + c = 0 ....(2)

from equations (1) and (2) we get,

f = -g ....(3)

now putting (12,0) in equation,

12² + 0² + 2g(12) + 2f(0) + c = 0

⇒144 + 24g + c = 0 ....(3)

from equations (1) and (3) we get,

g = -2

so, f = 2 [ from eq (3) ]

and c = -96

so the equation of circle is x² + y² - 4x + 4y - 96 = 0

centre of circle = (2, -2)

and radius of circle , r = √{(2)² + (-2)² - (-96)} = √104

so the area of circle = πr²

= π × 104

= 3.14 × 104

= 326.56 sq unit

Therefore the area of circle passing through the given points is 326.56 sq unit.

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