Question

B and c are fixed points having coordinates (3,0) and (-3,0) respectively. If the vertical angle bac is 90 then locus

Answer 1

Answer:

The required locus is

$\bf\:x^2+y^2=9$

Step-by-step explanation:

Given:

B(3,0) and C(-3,0)

Let A(h,k) be the moving point

As per given data,

∠BAC=90°

AB is perpendicular to AC

This implies,

$\text{(slope of AB)(slope of AC)=-1}$

$\impllies\frac{k-0}{h-3}*\frac{k-0}{h+3}=-1$

$\impllies\frac{k}{h-3}*\frac{k}{h+3}=-1$

$\impllies\frac{k^2}{(h-3)(h+3)}=-1$

$\impllies\frac{k^2}{h^2-9}=-1$

$\impllies\:k^2=-(h^2-9)$

$\impllies\:k^2=-h^2+9$

$\impllies\bf\:h^2+k^2=9$

$\therefore\text{The locus of A is }\bf\:x^2+y^2=9$