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From circle theorems, the tangent to a circle is perpendicular to the radius, and so to find the tangent we can use the gradient of the radius connecting the point (-3, -4) to the centre of the circle and...

(6² + 8²)^1/2 = (125a³ )^1/3(36+62)^1/2 = (125a³ )^1/3100^1/2 = (125a³ )^1/3+/- 10 = (125...

Observing that 48 = 24 * 2 = 1222 = 443, we can write square root of 48 as being square root of 443, which means that sqrt(48) = 22sqrt(3).Now, we can multiply the new ...

x(x-4)+y(y+6)+4=0x^2-4x+y^2+6y+4=0x^2-4x+4+y^2+6y+9=9(x-2)^2+(y+3)^2=9=3^2centre (2,-3) radius 3

I would let the student identify what the important elements of the question are and encourage them to assign each with a term or other mathematical notation. I would then go through these to make sure th...