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Maths Class 11 Chapter 11 Conic section part-1 Circles
Circles
Circle is defined as the locus of a point which moves in a plane such that its distance from a
fixed point in that plane is constant.
Standard Forms of a Circle
(i) Equation of circle having centre (h, k) and radius (x — h)2 + (y — k)2 = a2.
If centre is (0, 0), then equation of circle is x2 + y2 = a2.
(ii) When the circle passes through the origin, then equation of the circle is x 2 + y2 — 2hx —
2ky = 0.
(iii) When the circle touches the X-axis, the equation is x2 + y2 — 2hx — 2ay + h2 = O.
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(iv) Equation of the circle, touching the Y-axis is x2 + y2 — 2ax — 2ky + k2 = 0.
(v) Equation of the circle, touching both axes is x2 + y2 — 2ax — 2ay + a2 = O.
(vi) Equation of the circle passing through the origin and centre lying on the X-axis is x2 +
y2 — 2ax = O.
(vii) Equation of the circle passing through the origin and centre lying on the Y-axis is x2 + y2 –
2ay = 0.
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(viii) Equation of the circle through the origin and cutting intercepts a and b on the coordinate
axes is x2 + y2 — by = 0.
(ix) Equation of the circle, when the coordinates of end points of a diameter are (x1, y1) and (x2,
y2) is
(x — x1)(x — x2) + (y – y1)(y — y2) = 0.
(x) Equation of the circle passes through three given points (x 1, y1), (x2, y2) and (x3, y3) is
(xi) Parametric equation of a circle
(x – h)2 + (y – k)2 = a2 is
x = h + a cosθ, y = k + a sinθ,
0 ≤ θ ≤ 2π
For circle x2 + y2 = a2, parametric equation is
x = a cos θ, y = a sin θ
Maths Class 11 Chapter 11 Conic section part-1 Circles
Circles
Circle is defined as the locus of a point which moves in a plane such that its distance from a
fixed point in that plane is constant.
Standard Forms of a Circle
(i) Equation of circle having centre (h, k) and radius (x — h)2 + (y — k)2 = a2.
If centre is (0, 0), then equation of circle is x2 + y2 = a2.
(ii) When the circle passes through the origin, then equation of the circle is x 2 + y2 — 2hx —
2ky = 0.
(iii) When the circle touches the X-axis, the equation is x2 + y2 — 2hx — 2ay + h2 = O.
,2|Page
(iv) Equation of the circle, touching the Y-axis is x2 + y2 — 2ax — 2ky + k2 = 0.
(v) Equation of the circle, touching both axes is x2 + y2 — 2ax — 2ay + a2 = O.
(vi) Equation of the circle passing through the origin and centre lying on the X-axis is x2 +
y2 — 2ax = O.
(vii) Equation of the circle passing through the origin and centre lying on the Y-axis is x2 + y2 –
2ay = 0.
, 3|Page
(viii) Equation of the circle through the origin and cutting intercepts a and b on the coordinate
axes is x2 + y2 — by = 0.
(ix) Equation of the circle, when the coordinates of end points of a diameter are (x1, y1) and (x2,
y2) is
(x — x1)(x — x2) + (y – y1)(y — y2) = 0.
(x) Equation of the circle passes through three given points (x 1, y1), (x2, y2) and (x3, y3) is
(xi) Parametric equation of a circle
(x – h)2 + (y – k)2 = a2 is
x = h + a cosθ, y = k + a sinθ,
0 ≤ θ ≤ 2π
For circle x2 + y2 = a2, parametric equation is
x = a cos θ, y = a sin θ
