Question

Find the centre and radius of the circle x^2 + y^2 - 2x - 4y - 11 = 0​

Answer 1

Answer:

center=>(1.−2)

radius=

1+4+11

$\sqrt{16} = 14$

Answer 2

EXPLANATION.

Equation of the circle.

⇒ x² + y² - 2x - 4y - 11 = 0.

As we know that,

General equation of circle.

⇒ x² + y² + 2gx + 2fy + c = 0.

Centre of the circle = (-g,-f).

Compare both the equation, we get.

Centre of the circle = (1,2).

Radius of the circle = √g² + f² - c.

Radius of the circle = √(1)² + (2)² - (-11).

Radius of  the circle = √1 + 4 + 11.

Radius of the circle = √16 = 4.

                                                                                                                           

MORE INFORMATION.

Equation of normal.

(1) = The equation of normal to the circle x² + y² + 2gx + 2fy + c = 0 at any point (x₁, y₁) is,

⇒ y - y₁ = y₁ + f/x₁ + g (x - x₁).

(2) = The equation of normal to the circle x² + y² = a² at any point (x₁, y₁) is,

⇒ xy₁ - x₁y = 0.