IIT-JEE 1983Question 1
Given the points $A(0,4)$ and $B(0,-4)$, the equation of the locus of the point $P(x,y)$ such that $|AP-BP|=6$ is ______.
Hyperbola
Answer$\dfrac{y^{2}}{9}-\dfrac{x^{2}}{7}=1$
Solution
$|AP-BP|=6$ with foci $(0,\pm4)$: hyperbola with $a=3$, $c=4$, $b^2=7$, i.e. $\frac{y^2}9-\frac{x^2}7=1$.