The equation of a circle is
Work out the length of the diameter.
Circle your answer.
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The equation of a circle is
Work out the length of the diameter.
Circle your answer.
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The equation of a circle is
Work out the length of the diameter.
Circle your answer.
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Describe fully the graph which has the equation x2 + y2 = 9.
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A circle, centre , passes through (5, 0).
What is the equation of the circle?
Circle your answer.
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Work out the diameter of the circle
Circle your answer.
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Construct the graph of
By drawing the line on the grid, solve the equations
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The equation of a curve is
is the point where the curve intersects the -axis.
State the coordinates of .
The equation of circle is
The circle is translated by the vector to give circle .
Draw a sketch of circle .
Label with coordinates
the centre of circle
and any points of intersection with the -axis.
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On the grid, construct the graph of
Find estimates for the solutions of the simultaneous equations
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and are points on the circle as shown.
is on the -axis.
is on the -axis.
is the midpoint of .
is a straight line.
Show that the coordinates of are (0, 6).
Work out the coordinates of .
Show that the equation of the straight line passing through and is .
Work out the coordinates of .
Give your answers in surd form.
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(–1, 4) is a point on a circle, centre
Work out the equation of the tangent to the circle at .
Give your answer in the form .
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Here is a sketch of the circle
Show that the tangent to this circle at the point (-3, 6) has a gradient of
Find the equation of the tangent at the point (-3, 6).
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The point ( -5, 2 ) lies on the circumference of a circle, centre (0, 0).
Find the equation of the circle.
Work out the gradient of the tangent to the circle at (-5, 2).
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In this question all units are in cm.
A circle has equation
Write down the radius and centre of the circle.
radius: .......................................................... cm
centre: (..........................., ...........................)
The distinct points A () and B () lie on the circumference of the circle.
Work out the length AB.
................................................... cm
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Here is a circle, centre , and the tangent to the circle at the point (4, 3) on the circle.
Find an equation of the tangent at the point .
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On the grid, draw the graph of
Hence find estimates for the solutions of the simultaneous equation
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is the circle with equation
is a point on .
Find an equation of the tangent to at the point .
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The diagram shows a circle, centre the origin.
Write down the equation of the circle.
Point has coordinates (8, —6).
Show that point lies on the circle.
Find the equation of the tangent to the circle at point .
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A circle has equation x2 + y2 = 80.
Calculate the diameter of the circle.
Give your answer as a surd in its simplest form.
Colin says that the point (5, 7) lies outside the circle.
Is Colin correct?
Show your reasoning.
Show that the line with equation y = x + 10 is a tangent to the circle.
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is a point on the circle with equation
has -coordinate 4 and is below the -axis.
Work out the equation of the tangent to the circle at .
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The diagram shows the circle
lies on the circle and has -coordinate 1
The tangent at intersects the -axis at .
Work out the coordinates of Q.
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The diagram shows a circle with centre (0, 0) and a tangent at the point (–12, 16).
The tangent crosses the y-axis at the point (0, p).
Find the value of p.
p = .....................................................
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The diagram shows a circle, centre .
The circumference of the circle is 20π cm.
Find the equation of the circle.
The line 10x + py = q is a tangent at the point (5, 4) in another circle with centre (0, 0).
Find the value of p and the value of q.
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The line is a tangent to the circle at the point .
is the point (2, 6).
The line crosses the -axis at the point .
Work out the area of triangle .
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The diagram shows the circle x2 + y2 =5.
Mandy says that the point (2, 1.5) lies inside the circle.
Is she correct?
Show how you decide.
The tangent to the circle at the point P (-2, 1) intersects the y-axis at A.
Show that the area of the triangle APO is 5 square units.
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The diagram shows a circle, centre .
is the tangent to the circle at the point .
Angle
Point has coordinates (16, 0)
Point has coordinates (3p, p)
Find the value of p.
Give your answer correct to 1 decimal place.
You must show all your working.
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Prove algebraically that the straight line with equation is a tangent to the circle with equation
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In this question, all lengths are in centimetres.
is a point on a circle, centre .
is a point on a different circle, centre .
The equation of the larger circle is
radius of smaller circle : radius of larger circle = 4 : 5
Work out the size of angle
............................................ degrees
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(4, 8) is a point on a circle, centre .
The tangent at intersects the axes at points and .
Show that the gradient of the tangent is
Work out the length .
Give your answer in the form where is an integer.
You must show your working.
....................................units
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