Pearson Edexcel International A Level · Pure Mathematics (YPM01)

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

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

8 questions26 marksFree, no account

Question 1

1 mark

A straight line $L_1$ has the equation $3x + 6y = 5$. Find the gradient of a line $L_2$ that is perpendicular to $L_1$.

Question 2

1 mark

A circle $C$ has the equation $x^2 + y^2 - 10x + 4y - 20 = 0$. Find the coordinates of the centre and the radius of $C$.

Question 3

1 mark

A circle $C$ has the equation $(x - 4)^2 + (y + 1)^2 = 25$ . A line $L$ is tangent to $C$ at the point $P(7, 3)$ . Find the equation of the line $L$ .

Question 4

3 marks

A circle $C$ has the equation $(x+1)^2 + (y-3)^2 = 25$. Find the equation of the tangent to the circle at the point $P(2, 7)$, giving your answer in the form $ax + by + c = 0$.

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Question 5

4 marks

Line $L_1$ has the equation $2x + 3y = 7$. Line $L_2$ is perpendicular to $L_1$ and passes through the point of intersection of the lines $x - y = 1$ and $y = 5$. Find the equation of $L_2$, giving your answer in the form $ax + by + c = 0$, where $a$, $b$, and $c$ are integers.

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Question 6

4 marks

The line $ L_1 $ passes through the points $ A(1, 4) $ and $ B(5, 2) $. Find the equation of the line $ L_2 $ which is perpendicular to $ L_1 $ and passes through the point $ P(3, 1) $, giving your answer in the form $ ax + by + c = 0 $.

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Question 7

4 marks

The points $A$, $B$ and $C$ have coordinates $A(3, 1)$, $B(7, 4)$, and $C(p, 1)$, where $p$ is a constant.

Part (a)

Find the gradient of the line segment $AB$.

Part (b)

The line $L$ passes through $B$ and is perpendicular to $AB$. Find the equation of the line $L$, giving your answer in the form $ax + by + c = 0$, where $a, b,$ and $c$ are integers.

Part (c)

Given that the area of the triangle $ABC$ is 9 square units, find the possible values of $p$.

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Question 8

8 marks

The circle $C$ has the equation $x^2 + y^2 - 4x + 2y - 20 = 0$.
(a) Find the coordinates of the centre $M$ and the radius of $C$.
(b) The point $P(-1, 3)$ lies on the circle. Find the equation of the tangent to the circle at the point $P$, giving your answer in the form $ax + by + c = 0$, where $a, b,$ and $c$ are integers.
(c) The tangent at $P$ intersects the $x$-axis at the point $A$ and the $y$-axis at the point $B$. Find the area of the triangle $OAB$, where $O$ is the origin.
(d) There is another tangent to the circle $C$ that is parallel to the tangent found in part (b). Find the equation of this tangent in the form $ax + by + d = 0$.

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

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