Equation of a circle

A circle with centre C has equation

The graph with equation

y = │ 3 x – 36 │ – 8

intersects the circle at the points A, B and D as shown in the diagram.

Point D is vertically below point C

State the coordinates of C

State the coordinates of D

The coordinates of A are (a,10)

Find the value of a

Fully justify your answer.

Find, in radians, the angle ADB

Give your answer to three significant figures.

Hence or otherwise find the length of the minor arc AB

Give your answer to three significant figures.

The points P and Q have coordinates (6, 15) and (12, 19) respectively.

Find the coordinates of the midpoint of PQ

Find the equation of the perpendicular bisector of PQ

Give your answer in the form ax by c where a, b and c are integers.

A circle passes through the points P and Q

The centre of the circle lies on the line with equation 2x 5y 30

Find the equation of the circle.

The circle intersects the coordinate axes at n points.

State the value of n

A circle has equation

Find the radius of the circle.

Circle your answer.

4 12 16 256

The lines L₁ and L₂ are parallel.

L₁ intersects the y-axis at the point P.

The point Q is the point on L₂ closest to P, as shown in the diagram.

Find the coordinates of Q.

Hence show that PQ k34, where k is an integer to be found.

A circle, C, has centre (a, 17).

L₁ and L₂ are both tangents to C.

Find a.

Find the equation of C.

A circle has centre (4, 5) and radius 6

Find the equation of the circle.

Tick () one box.

A circle has equation

State the coordinates of the centre of the circle.

Find the radius of the circle in terms of p.

The circle intersects the coordinate axes at exactly three points.

Find the two possible values of p.

The line L has equation

A circle, C, has centre (7, 9)

L is a tangent to C.

Find the coordinates of the point of intersection of L and C.

Fully justify your answer.

Find the equation of C.

A circle has equation x² y² 6x 8y 264

AB is a chord of the circle.

The angle at the centre of the circle, subtended by AB, is 0.9 radians, as shown in the diagram below.

Find the area of the minor segment shaded on the diagram.

Give your answer to three significant figures.

Three points A, B and C have coordinates A (8, 17), B (15, 10) and C (2, 7)

Show that angle ABC is a right angle.

A, B and C lie on a circle.

Explain why AC is a diameter of the circle.

Determine whether the point D (8, 2) lies inside the circle, on the circle or outside the circle.

Fully justify your answer.

A company is designing a logo. The logo is a circle of radius 4 inches with an inscribed rectangle. The rectangle must be as large as possible.

The company models the logo on an x - y plane as shown in the diagram.

Use calculus to find the maximum area of the rectangle.

Fully justify your answer.

A circle has equation (x 4)² (y 4)² 9

What is the area of the circle?

Circle your answer.