Are you good at finding locus

Geometry Level 5

The base of a triangle passes through a fixed point P ( a , b ) P(a,b) and it's side's are bisected at right angle by the pair of straight line y 2 − 8 x y − 9 x 2 y^{2}-8xy-9x^{2} . The locus of its vertex is ω ( x 2 + y 2 ) + ( 4 a + 5 b ) x + 4 b − 5 a = 0 ω(x^{2}+y^{2})+(4a+5b)x+4b-5a=0 . Find ω ω .


The answer is 4.

Shivam Jadhav by Shivam Jadhav , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Aryan Goyat
Jan 10, 2016

we consider its vertex as (h,k) and find its reflection about the two lines (perpendicular bisector) given which will give the other 2 vertex of base ,let the two be P,Q we know that P,Q and (a,b) lie on same line so we make the area of triangle formed by the 3 points as 0.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...