Question

find the centre and radius of circle x2 + y2-2x+4y-4=0​

Answer 1

EXPLANATION.

Equation of circle.

⇒ x² + y² - 2x + 4y - 4 = 0.

As we know that,

General equation of circle.

⇒ x² + y² + 2gx + 2fy + c = 0.

Compare both the equation, we get.

⇒ Centre of circle = (-g,-f).

⇒ Centre of circle = (1,-2).

⇒ Radius of circle = √g² + f² - c.

⇒ Radius of circle = √(1)² + (-2)² - (-4).

⇒ Radius of circle = √1 + 4 + 4.

⇒ Radius of circle = √9 = 3.

                                                                                                                         

MORE INFORMATION.

General equation of circle.

(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.

Diametral form.

If (x₁ , y₁) and (x₂ , y₂) be the extremities of a diameter, then the equation of circle is,

(x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0.

Answer 2

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EXPLANATION.

Equation of circle.

⇒ x² + y² - 2x + 4y - 4 = 0.

As we know that,

General equation of circle.

⇒ x² + y² + 2gx + 2fy + c = 0.

Compare both the equation, we get.

⇒ Centre of circle = (-g,-f).

⇒ Centre of circle = (1,-2).

⇒ Radius of circle = √g² + f² - c.

⇒ Radius of circle = √(1)² + (-2)² - (-4).

⇒ Radius of circle = √1 + 4 + 4.

⇒ Radius of circle = √9 = 3.

                                                                                                                         

MORE INFORMATION.

General equation of circle.

(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.

Diametral form.

If (x₁ , y₁) and (x₂ , y₂) be the extremities of a diameter, then the equation of circle is,

(x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0.

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