Circles — Class 11 ISC Mathematics revision notes
A 3-page visual revision sheet for Circles, written for Class 11 ISC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Circles in one look
a centre, a radius, and what a line can do to them
Standard equation
- a circle: all points of a plane at a fixed distance r from a fixed point
- the fixed point is the centre, the distance the radius
- centre (h,k) and radius r fix the circle
- centre at the origin: x^2+y^2=r^2
Standard forms
- centre (h,k), radius r
(x-h)^2+(y-k)^2=r^2 - centre the origin
x^2+y^2=r^2 - ends of a diameter (x_1,y_1), (x_2,y_2)
(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0
Special positions
- Touches the X-axis: radius equals |k|
- Touches the Y-axis: radius equals |h|
- Touches both axes: |h|=|k|=r
- Passes through the origin: h^2+k^2=r^2
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Circles sheet covers
- Standard equation
- Standard forms
- centre (h,k), radius r
- centre the origin
- ends of a diameter (x_1,y_1), (x_2,y_2)
- Special positions
- Touches the X-axis
- Touches the Y-axis
- Touches both axes
- Passes through the origin
- General equation
- general form
- centre
- radius
- Reading the equation
- Tangent and normal
- tangent at (x_1,y_1) on x^2+y^2=r^2
- tangent at (x_1,y_1) on the general circle
- tangency of y=mx+c to x^2+y^2=r^2
- Length of a tangent
- Chord, length and midpoint
- Chords from the circle's own equation
- chord with midpoint (x_1,y_1)
- chord of contact of tangents from (x_1,y_1)
- T is S with x^2to xx_1, 2xto x+x_1 and the same for y
- Circle through three points
- The determinant form
- the circle through the three points: the determinant of the grid is zero
- Where a point sits
- Symbols
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Circles the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.