Write down the equations of the circles with the following centres and radii
Centre: (-5 , 0) Radius: r = 5.
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Write down the equations of the circles with the following centres and radii
Centre: (-5 , 0) Radius: r = 5.
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Write down the centre and the radius for each of the following circles
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On separate diagrams sketch the circles with the following equations
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The line segment connecting the two points (1 , 0) and (9 , 4) is the diameter of a circle.
Find the centre and radius of the circle.
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Determine if the circles with equations
intersect once, twice or not at all. Fully explain your answer.
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On a sketch show how a circle and a line can either have 0, 1 or 2 intersections.
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The line with equation intersects the circle with equation
at two distinct points.
Find the coordinates of the two points of intersection.
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A circle has centre (6, -5) and goes through the point (1, 7). Find the equation of the circle.
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Show that can be written in the form , where , and are integers to be found.
Hence write down the centre and radius of the circle with equation
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The linemeets the circle with equation .
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The lineintersects the circle at the points and . Find the coordinates of and .
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A circle has centre (-4, 1) and passes through the point (0, 3).
Find an equation for the circle .
Find an equation for the tangent to the circle at .
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The points and lie on a circle.
Show that triangle is a right-angle triangle.
Explain why the line segment must be the diameter of the circle.
Hence find the equation of the circle.
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Circles , and all have their centres on the -axis.
Circle has equation .
Circle has equation .
Circles and touch at point , and circles and touch at point .
Find the coordinates of the centre of circle .
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A circle has equation .
The lines and are both tangents to the circle, and they intersect at the origin.
Explain why the equations for and must each be in the form , where is the gradient of the line.
Show that the gradients of and must be the solutions to the equation
Hence find the equations of and , giving your answers in the form .
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The points A (-3, 1) and B (3, -7) are the two endpoints of the diameter AB of a circle. Find the equation of the circle.
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Show that can be written in the form , where and are constants to be found.
Hence write down the centre and radius of the circle with equation
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The line meets the circle with equation .
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The line intersects the circle at the points and . Find the coordinates of and
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A circle has centre (-2, 3) and passes through the point (6, -3).
Find an equation for the circle .
Find an equation for the tangent to the circle at P.
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The points and lie on a circle.
Show that
Deduce a geometrical property of the line segment AB.
Hence find the equation of the circle.
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Triangle has vertices (-8, 1), (12, 16) and (12, 1). A circle with equation touches Triangle at the three points and , as shown in the diagram below:
Write down the coordinates of points R and Q.
Find the coordinates of point P.
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A circle has equation
The lines and are both tangents to the circle, and they intersect at the point (0, 14).
Find the equations of and , giving your answers in the form .
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The points (2, -21) and (-5, 3) are the two endpoints of the diameter of a circle. Find the equation of the circle in the form , where and are integers to be found.
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Find the centre and radius of the circle with equation
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The line intersects the circle at exactly two points. Find the range of possible values of .
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The points (-2, 3), (0, 6) and (, -1) lie on a circle, where is the diameter of the circle.
Find the value of .
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A circle has equation Point lies on the circle, and the tangent to the circle at point has a gradient of -3. Find the two possible sets of coordinates for point .
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The pointsand lie on a circle.
Find the equation of the circle.
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A circle has equation
The lines and are both tangents to the circle, and they intersect at the point (5, 0).
Find the equations of and , giving your answers in the form .
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The diagram below shows circles and which intersect at the two points and . Circle has equation , and points and lie along the line with equation . Circle also passes through the point (-13, 2).
Find an equation of circle .
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