# MAT - Paper 2007 - Q1D

> Source: https://ollybritton.com/notes/maths/problems/mat/2007/q1d/ · Updated: 2021-10-14 · Tags: mat, notes, maths

## Flashcards
### 2021-10-14
##### Does the line $y = \frac{3}{4}x$ go through the circle $$(x - 1)^2 + (y - 1)^2 = 1$$??
No way Jose.

##### ![PHOTO TWO CIRCLES](two-circles.png) 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??
$$
\left(\begin{matrix} 4 \\\\ 3 \end{matrix}\right)
$$

##### ![PHOTO TWO CIRCLES](two-circles.png) 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.

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