namenerk
2021-12-12
Answered

A point moves so that the angle from the line joining it and the origin to the line (3, - 2) and (5, 7) is $45}^{\circ$ Find the equation of the locus.

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Jacob Homer

Answered 2021-12-13
Author has **41** answers

Step 1

Let the coordinate of the moving point be

Then slope of the line joining this two point

and the slope of the line joining the point (3, -2) and (5, 7) is

Now given that the above two lins whose slope are

Then by angle between two lines formula

When we remove moduls it will give + and -, (Taking + for actuale angle

When + Then

Donald Cheek

Answered 2021-12-14
Author has **41** answers

Step 1

Then, according to the formula for the angle between two lines

${\mathrm{tan}45}^{\circ}=\left|\frac{{m}_{1}-{m}_{2}}{1+{m}_{1}{m}_{2}}\right|$

$I=\left|\frac{{m}_{1}-{m}_{2}}{1+{m}_{1}{m}_{2}}\right|$

If we remove modules, there will be + and -

Then$1=\frac{{m}_{1}-{m}_{2}}{1+{m}_{1}{m}_{2}}$

$1+{m}_{1}{m}_{2}={m}_{1}-{m}_{2}$

$1+\frac{\beta}{\alpha}\times \frac{9}{2}=\frac{\beta}{\alpha}-\frac{9}{2}$

$2\alpha +9\beta -2\beta -9\alpha$

$11\alpha +7\beta =0$

The locus of the point will be

$11x+7y=0$

Then, according to the formula for the angle between two lines

If we remove modules, there will be + and -

Then

The locus of the point will be

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