Maths-Pure-Circles

Question 1

Equation of a Circle

Answer 1

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

Question 2

Centre and Radius

Answer 2

Centre is the opposite sine of the brackets e.g (x-2) and (y+3) centre equals (2,-3).

Radius is square root of r^2

Question 3

Completing the square

Answer 3

When in the form x^2 + y^2 + 2fx + 2gy + c you complete the square to find the equation and then further use to find the centre and radius.

Question 4

Properties of circles

Answer 4

Angle in a semi-circle is equal to 90 degrees
The perpendicular from the centre to a chord bisects the chord
A radius and tangent to the same point will meet at right angles

Question 5

Gradient Rule ( Perpendicular)

Answer 5

Tangent at a given point will be perpendicular.

Find the gradient of the radius using y2-y1/ x2-x2

Negative reciprocal
Then using line graph y-y1=m(x-x1)
Then rearrange to vy+vx-v=0

Question 6

Distance equation

Answer 6

Square root (x2-x1)^2 +(y2-y1)^2