Circle 4 Question 21
21. Let a given line intersect the and -axes at and respectively. Let another line , perpendicular to , cut the and -axes at and , respectively. Show that the locus of the point of intersection of the line and is a circle passing through the origin.
(1987, 3M)
Show Answer
Solution:
- Let the equation of
be .
Then, any line perpendicular to
where,
Then,
Similarly,
Now, equation of
Similarly, equation of
Locus of point of intersection of