Help with Locus questions! (1 Viewer)

Maancis · Sep 4, 2016

Can anyone help me out and explain how to do these questions! I know the answers but i don't understand how to actually show working for it

1) Find the equation of the locus so that the perpendicular distance from the x axis is twice the perpendicular distance from the y-axis

2) Find the equation of the locus so that the perpendicular distance from the x-axis is 3 less than the perpendicular distance from the y axis

Thankyou in advance

InteGrand · Sep 4, 2016

Maancis said:
Can anyone help me out and explain how to do these questions! I know the answers but i don't understand how to actually show working for it

1) Find the equation of the locus so that the perpendicular distance from the x axis is twice the perpendicular distance from the y-axis

2) Find the equation of the locus so that the perpendicular distance from the x-axis is 3 less than the perpendicular distance from the y axis

Thankyou in advance

$\noindent 1) A point $P(x,y)$ lies on the locus iff $|y| = 2|x|$ (since $|y|$ is the distance of $P$ from the $x$-axis, and similarly $|x|$ for the $y$-axis). So the locus is the pair of interesting lines $ y = \pm 2x$.$

$\noindent 2) A point $P(x,y)$ lies on the locus iff $|y| = |x|-3$, which is the equation of the locus. We can also write it as $y = \pm \left(|x| -3\right)$.$

Help with Locus questions! (1 Viewer)

Maancis

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InteGrand

Well-Known Member

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