find the equation of ap circle passing through point 2,3 whose centre is h,k and radius is 4cm?
Answers
EXPLANATION.
Equation of circle passing through the point = (2,3).
Centre is h, k and radius = 4.
As we know that,
General equation of circle,
⇒ x² + y² + 2gx + 2fy + c = 0.
We can write this equation as,
⇒ (x - h)² + (y - k)² = (r)².
Centre = (2,3).
Radius = 4.
Put the values in the equation, we get.
⇒ (x - 2)² + (y - 3)² = (4)².
As we know that,
Formula of :
⇒ (x - y)² = x² + y² - 2xy.
Using this formula in equation, we get.
⇒ x² + 4 - 4x + y² + 9 - 6y = 16.
⇒ x² + y² - 4x - 6y + 4 + 9 - 16 = 0.
⇒ x² + y² - 4x - 6y - 3 = 0.
MORE INFORMATION.
The parametric equation of circle.
(1) = The parametric equation of a circle : x² + y² = r² are,
⇒ x = r cosθ & y = r sinθ.
(2) = The parametric equation of the circle : (x - h)² + (y - k)² = r² are,
⇒ x = h + r cosθ & y = k + r sinθ.
(3) = Parametric equations of the circle : x² + y² + 2gx + 2fy + c = 0 are,
⇒ x = - g + √g² + f² - c cosθ.
⇒ y = - f + √g² + f² - c sinθ.