find the centre and radius of the circle whose equation is given by x2+y2-4x-8y-45 =0
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EXPLANATION.
Equation of the circle.
⇒ x² + y² - 4x - 8y - 45 = 0.
As we know that,
General equation of the circle.
⇒ x² + y² + 2gx + 2fy + c = 0.
Compare both the equations, we get.
Center of the circle = (-g,-f).
Center of the circle = (2,4).
Radius of the circle = √(g)² + (f)² - c.
⇒ √(2)² + (4)² - (-45).
⇒ √4 + 16 + 45.
⇒ √65.
Radius of the circle = √65.
MORE INFORMATION.
General equation of the circle represents.
(1) = A real circle if, g² + f² - c > 0.
(2) = A point circle, if g² + f² - c = 0.
(3) = An imaginary circle, if g² + f² - c < 0.
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