Intersection in or Inside a Circle

Find the x intercepts of the graph of the circle given by the equation

x ² + 3x + y ² - 4y = 18

Write the intercepts as coordinates

Is point A(-3 , 8) inside, outside or on the circle whose equation is given by

x ² + 4x + y ² - 8y = 5

• Inside the circle

• Outside the circle

• On the circle

Find the points of intersection of the circle with equation

(x - 2) ² + (y - 6) ² = 40

and the line with equation y = 3x

The diagram shows two circles with centres O and P. Given OP = 4 cm, S is the midpoint of OP and Q is the midpoint of SP.

A point L moves such that it is always 3 cm from point O. A point M moves such that it is always 2 cm from point P.

Which of the following points are the intersection of locus L and locus M?

• S and T

• Q and R

• R and T

• P and T

• a

• b

• c

• d

In the diagram, PQRS is a square. PTR is an arc of a circle with centre S. QUS is an arc of a circle with centre P.

X is the locus of a point which moves such that its distance from S is always constant. Y is the locus of a point which moves such that it is equidistant from the lines PQ and QR. Which of the points, A, B, C or D, is the intersection of the locus X and the locus Y?

• A

• B

• C

• D

The diagram shows a circle with centre O and a radius of 5 cm. The circle is divided into 8 equal parts.

Which two points are intersections of two loci which are always 5 cm from point O and 5 cm from the line LOQ?

• L and Q

• N and S

• M and R

• K and P

In the diagram, PQR is an equilateral triangle with sides of 4 cm. UM and KL are two circular arcs with Q as the centre. K is the midpoint of UP.

X is the locus of a point which moves such that its distance from Q is always 3 cm. Y is the locus of a point which moves such that YQ = YR. The point of intersection of the locus X and locus Y is

• N

• P

• M

• L

In the diagram, MN and RS are two circular arcs with a common centre O and with radii 4 cm and 8 cm respectively.

OT is the bisector of ∠ROS. A point P moves such that it is more than 4 cm but less than 8 cm from point O, and is always equidistant from lines OR and OS.

Which of the points, A, B, C or D, is a possible position of point P ?

• A

• B

• C

• D

In the diagram, P and Q are centres of two circles. Which of the points, A, B, C or D, is 5 cm from P and less than 3 cm from Q?

• A

• B

• C

• D