# Thread: line and circle equations

1. ## line and circle equations

the points A and B lie on a circle with centre P, as shown in figure 3.
the point A has coordinates (1,-2) and the midpoint M of AB has coordinates (3,1).
The line l passes through the points M and P.

a)find an equation for l.

Given that the x-coordinate of P is 6,

b) use your answer to part (a) to show that the y-coordinate of P is -1
(i could do this bit if i had the equation)

c) find an equation for the circle

2. Originally Posted by kls7162

the points A and B lie on a circle with centre P, as shown in figure 3.
the point A has coordinates (1,-2) and the midpoint M of AB has coordinates (3,1).
The line l passes through the points M and P.

a)find an equation for l.

...
The line l is perpendicular to AM and passes through M.

1. Calculate the slope of AM:

$\displaystyle m_{AM} = \frac{1-(-2)}{3-1}=\frac32$

Therefore the slope of the line l is $\displaystyle m_l = -\frac23$

Now use point-slope-formula to get the equation of l:

$\displaystyle y-1 = -\frac23 (x-3)~\implies~ \boxed{y = -\frac23 x +3}$

I'll leave the rest for you.

3. ## Circles

for par A use slope point form $\displaystyle y-f(x_0)=m(x-x_0)$ and to get m just use $\displaystyle m=\frac{\Delta{y}}{\Delta{x}}$

### the points a an

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