Question

find the value of k if the didtance between the points (2,k) and (4,3) is 8

Answer 1

We Know by The Formula for distance Between two points
√(x₁ - x₂)² + (y₁ - y₂)² 
So,√(2 - 4)² + (k-3)² = 8
squaring on BS
(2)² + k² + 3² - 6k =64
k² -6k -51=0
BY using Quadratic equation formula
k=(-(-6) [+/-]√(6)² - 4(-51)) /2 = 10.746 or - 4.746
Here Both Satisfys the Eq.

Answer 2

distance formula=square root (x2-x1)2-(y2-y1)2
square root (4-2)2+(3-k)2=8
square root 4+9+k2-6k=8
square root 13+k2-6k=8
k2-6k+13=64
k2-6k-64+13=0
k2-6k-51=0
Here, a=1,b=-6,c=-51
Formula= [-b (+/-)square root (b2-4ac)]/2a
On solving we get,
two values= 10.74 or -4.74
so the value of k=10.74
As the other one is in negative we 'll not take it..

Hope it's helpful!!!