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If the lines 2x − 3y = 5 and 3x − 4y = 7 are the diameters of a circle of area 154 square units, then obtain the equation of the circle.
Concept: undefined >> undefined
If the line y = \[\sqrt{3}\] x + k touches the circle x2 + y2 = 16, then find the value of k.
Concept: undefined >> undefined
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Find the equation of the circle having (1, −2) as its centre and passing through the intersection of the lines 3x + y = 14 and 2x + 5y = 18.
Concept: undefined >> undefined
If the lines 3x − 4y + 4 = 0 and 6x − 8y − 7 = 0 are tangents to a circle, then find the radius of the circle.
Concept: undefined >> undefined
Show that the point (x, y) given by \[x = \frac{2at}{1 + t^2}\] and \[y = a\left( \frac{1 - t^2}{1 + t^2} \right)\] lies on a circle for all real values of t such that \[- 1 \leq t \leq 1\] where a is any given real number.
Concept: undefined >> undefined
The circle x2 + y2 − 2x − 2y + 1 = 0 is rolled along the positive direction of x-axis and makes one complete roll. Find its equation in new-position.
Concept: undefined >> undefined
One diameter of the circle circumscribing the rectangle ABCD is 4y = x + 7. If the coordinates of A and B are (−3, 4) and (5, 4) respectively, find the equation of the circle.
Concept: undefined >> undefined
If the line 2x − y + 1 = 0 touches the circle at the point (2, 5) and the centre of the circle lies on the line x + y − 9 = 0. Find the equation of the circle.
Concept: undefined >> undefined
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
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
