What is covered in Grade 11 Mathematics Analytical Geometry?

Equation of a line. Inclination angle. Distance from a point to a line. Coordinate geometry problems.

Is Grade 11 Analytical Geometry tested in Paper 1 or Paper 2?

Grade 11 Mathematics Analytical Geometry is assessed in Paper 2 of the end-of-year examinations, as per the CAPS Mathematics curriculum guidelines.

When is Analytical Geometry taught in Grade 11 Mathematics?

Analytical Geometry is taught in Term 2 of Grade 11 according to the CAPS Annual Teaching Plan (ATP) for Mathematics in South Africa.

Is Grade 11 Mathematics Analytical Geometry on the CAPS curriculum?

Yes. Analytical Geometry is part of the official CAPS Mathematics curriculum for Grade 11, Term 2 in South Africa. The content on MathSciBuddy follows the Annual Teaching Plan (ATP) set by the Department of Basic Education.

Is this Grade 11 Mathematics study material free?

Yes. All chapter notes, definitions, formulas, and worked examples on MathSciBuddy are completely free to read. No account or subscription is needed to access CAPS-aligned study notes.

Grade 11 Mathematics

Grade 11 · Term 2Mathematics

Analytical Geometry

We extend Grade 10 analytical geometry to the equation of a circle centred at the origin and at any point, and find tangent lines to circles.

Week 1

4.1 Equation of a Circle & Tangent Lines

Write and use the equation of a circle $x^2+y^2=r^2$
Write and use $(x-a)^2+(y-b)^2=r^2$ (circle with centre $(a,b)$)
Find the equation of a tangent to a circle at a given point

🌍

Real-World Connection

Satellite orbits are circular (or elliptical). The equation of a circle precisely describes every point at distance $r$ from the centre — a GPS satellite at orbit radius $r$ satisfies exactly this equation in a 2D cross-section.

Circle centred at origin

x^2 + y^2 = r^2

$r$ = radius; every point $(x,y)$ satisfies this

Circle centred at $(a,b)$

(x-a)^2 + (y-b)^2 = r^2

Centre $(a,b)$, radius $r$

Property / Rule

Tangent to a Circle

A tangent at point $P(x_1, y_1)$ on the circle is PERPENDICULAR to the radius at $P$ . To find it: (1) find gradient of radius $OP$ , (2) gradient of tangent = negative reciprocal, (3) use point-gradient form.

m_{\text{radius}} \cdot m_{\text{tangent}} = -1

💡 Tip

To check if a point lies ON the circle, substitute its coordinates into the circle equation. If LHS = RHS, the point is on the circle.

Worked Examples

Worked Example

Find equation and tangent

Problem

(2,-3)

Activity — 8 Questions

CAPS Cognitive Level Distribution

L1 · Knowledge2 Q

L2 · Routine Procedures2 Q

L3 · Complex Procedures2 Q

L4 · Problem Solving2 Q

L1 · Knowledge1 mark

Write the equation of a circle with centre

(0,0)

and radius 7.

L1 · Knowledge2 marks

State the centre and radius of

(x-3)^2+(y+1)^2=16

L2 · Routine Procedures2 marks

Does the point

(3,4)

lie on

x^2+y^2=25

L2 · Routine Procedures2 marks

Find the equation of the circle with centre

(-2,4)

and radius

\sqrt{10}

L3 · Complex Procedures4 marks

Find the equation of the tangent to

x^2+y^2=50

P(5,5)

L3 · Complex Procedures4 marks

Rewrite

x^2+6x+y^2-4y=3

in standard circle form and state the centre and radius.

L4 · Problem Solving4 marks

Find the length of the tangent from external point

(8,0)

to the circle

x^2+y^2=16

L4 · Problem Solving5 marks

Circle

C_1

x^2+y^2=25

and

C_2

(x-8)^2+y^2=9

. How many points do they share?

Functions