Pearson Edexcel International AS Level · Pure Mathematics (XPM01)

Coordinate geometry in the (x, y) plane: Practice Questions

5 multiple-choice questions marked as you go, and 3 written questions with worked solutions. All on Coordinate geometry in the (x, y) plane.

8 questions14 marksFree, no account

Question 1

1 mark

A straight line passes through the point \((1, 2)\) and is parallel to the line with equation \(y = 4x - 5\). Find the equation of this line.

Question 2

1 mark

The points \( A(1, 2) \) and \( B(5, 8) \) are the endpoints of a diameter of a circle. Find the equation of this circle.

Question 3

1 mark

A circle C has the equation \(x^2 + y^2 - 10x + 4y + k = 0\), where \(k\) is a constant. The line \(l\) with equation \(y = 2x - 1\) is a tangent to the circle C at the point P. Find the coordinates of P and the value of \(k\).

Question 4

1 mark

A circle has the equation \( (x + 3)^2 + (y - 5)^2 = 16 \). Find the coordinates of the center and the length of the radius of the circle.

Question 5

1 mark

Find the possible values of the constant \(k\) such that the line with equation \(y = 2x + k\) is a tangent to the circle with equation \(x^2 + y^2 = 5\).

Question 6

2 marks

A circle is defined by the equation \( (x + 5)^2 + (y - 2)^2 = 49 \).
State the coordinates of the centre of the circle and calculate its radius.

Write your answer out first, then check it against the worked solution.

Question 7

4 marks

The circle \( C \) has centre \( (3, 4) \). The point \( P(7, 7) \) lies on the circumference of \( C \).
Find the equation of the tangent to the circle at the point \( P \), giving your answer in the form \( ax + by + c = 0 \).

Write your answer out first, then check it against the worked solution.

Question 8

3 marks

Line \( L_1 \) passes through the points \( (0, 4) \) and \( (2, 0) \).
Find the equation of \( L_1 \) in the form \( ax + by + c = 0 \), where \( a, b, \) and \( c \) are integers.

Write your answer out first, then check it against the worked solution.

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