Find the equlation of the cricle passing through the point (1,2)and having its center at (2,3).
Answers
EXPLANATION.
Equation of a circle passing through point (1,2).
Having a Centre = (2,3).
As we know that,
Formula of Equation of circle.
The equation of a circle having Centre (h, k) and radius r, is.
⇒ (x - h)² + (y - k)² = r².
We can write equation as,
Centre = (2,3) = (h, k).
⇒ (x - 2)² + (y - 3)² = r².
⇒ (1 - 2)² + (2 - 3)² = r².
⇒ (-1)² + (-1)² = r².
⇒ 1 + 1 = r².
⇒ r² = 2.
Now, we can write equation as,
⇒ (x - 2)² + (y - 3)² = r².
⇒ (x - 2)² + (y - 3)² = 2.
⇒ x² + 4 - 4x + y² + 9 - 6y = 2.
⇒ x² + y² - 4x - 6y + 13 = 2.
⇒ x² + y² - 4x - 6y + 13 - 2 = 0.
⇒ x² + y² - 4x - 6y + 11 = 0.
MORE INFORMATION.
The parametric equation of a 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 a circle x² + y² + 2gx + 2fy + c = 0 are x = - g + √g² + f² - c cosθ , y = - f + √g² + f² - c sinθ.