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.
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.
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date: 2021-10-14 18:54
summary: what are the coordinates of the point at the shortest distance between these two circles?
tags:
- '@?public'
- '@?mat'
- '@?notes'
- '@?maths'
title: MAT - Paper 2007 - Q1D
