always 2a units. Find the equation to the locus
of the moving point.
Answer:
Step-by-step explanation:
Let P be the moving point and the given points be A (c,0) and B (-c, 0). If (h, k) be the co-ordinates of any position of P on its locus then:
PA + PB = 2a
PA = 2a - PB
PA² = 4a² + PB² – 4a ∙ PB
PA² – PB² = 4a² – 4a ∙ PB
[(h - c)² +(k - 0)²] - [(h + c)² +(k - 0)²] = 4a² – 4a. PB
-4hc = 4a² – 4a∙PB
a ∙ PB = a² + hc
Taking square
a² ∙ PB² = (a² + hc)²
a² [(h + c)² + (k - 0)²] = (a² + hc)²
a² [h² + c² + 2hc + k²] = a⁴ + 2a²hc + h²c²
a²h² – h²c² + a²k² = a⁴ – a²c²
(a² – c²)h² + a²k² = a² (a² – c²)
h²/a² + k²/(a² – c²) = 1
Therefore, the required equation to the locus of P is
B) 35
C)39
D)40
Answer:
Step-by-step explanation:
From 1 to 10 we have 4 numbers which are {2,4,6,8}
From 10 to 20 we have 4 numbers which are {12,14,16,18}
.
.
.
From 70 to 78 we have 4 numbers which are {72,747,6,78}
conclusion: we 4×8 number = 32
Its formula
etc.
(30 pts)
Answer:
function
A set of ordered pairs where each first element is paired with one and only one second element and no element in either pair is without a partner.
Step-by-step explanation:
Question 1: Calculate the slope, x-intercept and y-intercept of a linear equation, f(x) = 5x + 4 ?
Solution:
Given,
f(x) = 5x + 4
The general form of a linear equation is,
f(x) = mx + c
So,
Slope = m = 5
Substitute f(x) = 0,
0 = 5x + 4
5x = -4
x = −45
The x-intercept is (−45, 0)
Substitute x = 0,
f(x) = 5(0) + 4
f(x) = 0 + 4
f(x) = 4
The y-intercept is (0,4)
Answer:
function junction
Step-by-step explanation: