MAT - Paper 2007 - Q1D


Flashcards

Shortest distance between two circles

Does the line $y = \frac{3}{4}x$ go through the circle

\[(x - 1)^2 + (y - 1)^2 = 1\]

?

No way Jose.

These are the circles

\[(x - 1)^2 + (y - 1)^2\]

and

\[(x - 5)^2 + (y - 4)^2 = 4\]

What is the vector for moving from the little circle to the big circle?

\[\left(\begin{matrix} 4 \\\\ 3 \end{matrix}\right)\]

If the vector for moving between the centre of each of the two circles (Dad) is

\[\left(\begin{matrix} 4 \\\\ 3 \end{matrix}\right)\]

(magnitude $5$), then what fraction of the journey is taken up by moving out of the first circle and up to the outside of the second circle?

\[\frac{3}{5}\]

When a coordinate geometry problem is getting tricky and you’re not allowed a calculator (i.e. the quadratic isn’t clearly factorisable or you’re having to substitute $y = \frac{3}{4}x + \frac{1}{4}$) then what could be an alternate way of tackling the problem?

Using vectors.