May/June 2026 Paper 13

2026 · 11 questions · 23 parts · 75 marks

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11(a)11(b)11(c)

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Context for question 11

Graph showing a circle centred on the positive $y$-axis with two tangent lines, $L_{1}$ and $L_{2}$, that cross just above the circle; $L_{1}$, the less steep right-hand tangent, meets the $y$-axis above the circle at $P$ and the $x$-axis to the right of the origin at $Q$; $L_{2}$, the steeper left-hand tangent, meets the $x$-axis to the left of the origin at $S$ and the $y$-axis below the circle at $R$; the origin $O$ lies on the $x$-axis between $S$ and $Q$.

The diagram shows a circle with two tangents,

L_{1}

and

L_{2}

. The tangent

L_{1}

intersects the

x

-axis at

Q

and the

y

-axis at

P

. The tangent

L_{2}

intersects the

x

-axis at

S

and the

y

-axis at

R

.

11(a)Coordinate Geometry CirclesMedium3 marks

The end-points of a diameter of the circle are

(0, 4 - 10)

and

(0, 4 + 10)

.

Show that the equation of the circle can be expressed as

x^{2} + y^{2} - 8 y + 6 = 0.

Draw with the mouse or a finger.

11(b)Coordinate Geometry CirclesHard4 marks

The two tangents,

L_{1}

and

L_{2}

, have equations of the form

y = - 3 x + c

.

Show that

c^{2} - 8 c - 84 = 0.

Draw with the mouse or a finger.

11(c)Straight Line Coordinate GeometryHard5 marks

Find the exact area of quadrilateral

P QR S

.

Working

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