Question

if the distance of the point(a,b) from(-3,0) as well as(3,0) are 4each,find a and b

Answer 1

X(-3,0)
Y(3,0)
A(a,b)

by sectional formula:
XA = 4 = √[(-3-a)²+(0-b)²]
16 = 9 + a² + 6a + b²
7 = a² + 6a + b² ___ (i)
YA = 4 = √[(3-a)²+(0-b)²]
16 = 9 + a² - 6a + b²
7 = a² - 6a + b² ___ (ii)
from (i) and (ii)
a² + 6a - b² = a² - 6a + b²
6a = - 6a
a = -a
a + a = 0
2a = 0
therefore a = 0
putting a = 0 in (i):
0² + 6*0 + b² = 7
b² = 7
b = ±√7

therefore A is at (0,√7) or (0,-√7)

Answer 2

Answer:

hope it will help you ☺️☺️