# Find the equation of straight line having a gradient of -#1/t# and passing through the point(#t^2#,2t).(pls see details below). ?

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This line meets the line 2y+x=4+2#t^2# at the point P.

Show that the x-coordinates of P is 2t(t-1) and find the y-coordinates of P.

Find the locus of P as t varies.

This line meets the line 2y+x=4+2

Show that the x-coordinates of P is 2t(t-1) and find the y-coordinates of P.

Find the locus of P as t varies.

##### 1 Answer

See below

#### Explanation:

If you know the slope

In your case,

we may rewrite this equation as

The other line is

(I just solved for

To find the point where the lines meet, let's ask for both equation to be satisfied. Since we know the expression for

Solving for

The last thing we need to do is to observe that

and thus the expression becomes

as required.