p311 q12
question : a variable line passing through the point (5,0) intersects the lines 3x-4y=0 and 3x+4y=0 at H and K respectively. Find the equation of the locus of the mid-point of HK.
thanks in advance
Hello,
Let and
The equation of the variable line is :
But we know that it's passing through (5,0).
Thus
-->
Therefore, the equation of the variable line is : , a is the variable
So we know that :
Because H and K are on this line.
Plus, H is on the line of equation
And K is on the line of equation
--->
By substituting (1) into (3), you will have with respect to a.
Replace this expression of in (1) to have with respect to a.
Do the same for and .
Then, the midpoint of HK is , which will be coordinates with respect to a
Hope that helps... If you have questions about some steps, don't hesitate ^^