Write the Equation of Circle & Explain it . (5 × 1=5) Draw the sketch the graph (a) X² + y² = 5... please explain with proper steps
Answers
EXPLANATION.
Equation of the circle.
General equation of the circle.
x² + y² + 2gx + 2fy + c = 0.
Center of circle = (-g,-f).
Radius of the circle = √g² + f² - c.
The general equation of second degree.
ax² + by² + 2hxy + 2gx + 2fy + c = 0. represents a circle if a = b ≠ 0 and h = 0.
General equation of circle represents.
(A) = A real number, if g² + f² - c > 0.
(B) = A point circle, if g² + f² - c = 0.
(C) = An imaginary circle, if g² + f² - c < 0.
Central form of the equation of a circle.
(1) = The equation of a circle having center (h, k) and radius r, is
(x - h)² + (y - k)² = r².
(2) = If the center is origin then the equation of a circle is,
x² + y² = r².
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.
The sketch graph of the circle.
x² + y² = 5.
Equation of circle having center is at origin,
x² + y² = r².
Compare both the equation, we get.
Center of circle = (-g,-f) = (0,0).
Radius of circle = √5.
