A(1,2) and B(7,10) are two points If P(x) is a point such that the angle APB is 60 degree - Maths - Straight Lines

Question

A(1,2) and B(7,10) are two points If P(x) is a point such that the
angle APB is 60 degree and the area of the triangle APB is maximum,
then which of the following is (are) correct?

A) P lies on the straight line 3x+4y=36
B) P lies on any line perpendicular to AB
C) P lies on the right bisector AB
D) P lies on the circle passing through the points (1,2) and (7,10)
and having a radius of 10 units

IT IS MULTICORRCT QUESTION

Neha Sethi · Accepted Answer

Dear student
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_59ba1055d8d3f%20png"
style="width: 273px; height: 216px;">

Since base AB of the △ is fixed,so for maximum  area of △PAR,height of △ should be maximum,this  is possible only when P lieson the ⊥ bisector of AB
Equation of ⊥ bisector of AB isy-6=-1-72-10x-4y-6=-34x-44y-24=-3x+123x+4y-36=0Also AB=10⇒AL=5So, AH=AL cosec60°=103
Correct options are: C and A
Regards