How do you do this: Find the area enclosed by the locus of all points that are exactly 1/3 as far away from the point (1,2) as they are from the line y=-2x+24?
I know this is talking about an ellipse using the definition of foci and directrix but I don't know where to start since this is not in standard position.
I know this is talking about an ellipse using the definition of foci and directrix but I don't know where to start since this is not in standard position.
1 Answer
Explanation:
Much of the key to solving this problem is in drawing what you know. For example, you are given the line
We are told that something ("the locus of all points") is one third as far the distance between the point
It would be perpendicular and, thus, have a slope that is perpendicular to the line, as well as pass through
The distance formula between
One third that distance is simply
The way I'm reading the question, the "area enclosed by all points" that have exactly the same distance from the center (i.e., one third the distance from center to line), is a circle.