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Find the coordinates of the centre and radius of each of the following circles: x2 + y2 + 6x − 8y − 24 = 0
Concept: undefined >> undefined
Find the coordinates of the centre and radius of each of the following circles: 2x2 + 2y2 − 3x + 5y = 7
Concept: undefined >> undefined
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Find the coordinates of the centre and radius of the following circle:
1/2 (x2 + y2) + x cos θ + y sin θ − 4 = 0
Concept: undefined >> undefined
Find the coordinates of the centre and radius of each of the following circles: x2 + y2 − ax − by = 0
Concept: undefined >> undefined
Find the equation of the circle passing through the points:
(5, 7), (8, 1) and (1, 3)
Concept: undefined >> undefined
Find the equation of the circle passing through the points:
(5, −8), (−2, 9) and (2, 1)
Concept: undefined >> undefined
Find the equation of the circle passing through the points:
(0, 0), (−2, 1) and (−3, 2)
Concept: undefined >> undefined
Find the equation of the circle which passes through (3, −2), (−2, 0) and has its centre on the line 2x − y = 3.
Concept: undefined >> undefined
Find the equation of the circle which passes through the points (3, 7), (5, 5) and has its centre on the line x − 4y = 1.
Concept: undefined >> undefined
Show that the points (3, −2), (1, 0), (−1, −2) and (1, −4) are concyclic.
Concept: undefined >> undefined
Show that the points (5, 5), (6, 4), (−2, 4) and (7, 1) all lie on a circle, and find its equation, centre and radius.
Concept: undefined >> undefined
Find the equation of the circle which circumscribes the triangle formed by the lines x + y + 3 = 0, x − y + 1 = 0 and x = 3
Concept: undefined >> undefined
Find the equation of the circle which circumscribes the triangle formed by the lines 2x + y − 3 = 0, x + y − 1 = 0 and 3x + 2y − 5 = 0
Concept: undefined >> undefined
Find the equation of the circle which circumscribes the triangle formed by the lines
x + y = 2, 3x − 4y = 6 and x − y = 0.
Concept: undefined >> undefined
Find the equation of the circle which circumscribes the triangle formed by the lines y = x + 2, 3y = 4x and 2y = 3x.
Concept: undefined >> undefined
Prove that the centres of the three circles x2 + y2 − 4x − 6y − 12 = 0, x2 + y2 + 2x + 4y − 10 = 0 and x2 + y2 − 10x − 16y − 1 = 0 are collinear.
Concept: undefined >> undefined
Prove that the radii of the circles x2 + y2 = 1, x2 + y2 − 2x − 6y − 6 = 0 and x2 + y2 − 4x − 12y − 9 = 0 are in A.P.
Concept: undefined >> undefined
Find the equation of the circle which passes through the origin and cuts off chords of lengths 4 and 6 on the positive side of the x-axis and y-axis respectively.
Concept: undefined >> undefined
Find the equation of the circle concentric with the circle x2 + y2 − 6x + 12y + 15 = 0 and double of its area.
Concept: undefined >> undefined
Find the equation to the circle which passes through the points (1, 1) (2, 2) and whose radius is 1. Show that there are two such circles.
Concept: undefined >> undefined
