Answer:
.
Step-by-step explanation:
If (α, β) are the coordinates of the center of the hyperbola, then its equation of the hyperbola is .
Now, the vertices of the hyperbola are given by (α ± a, β) ≡ (1,-3) and (-3,-3)
Hence, β = - 3 and α + a = 1 and α - a = -3
Now, solving those two equations of α and a we get,
2α = - 2, ⇒ α = -1 and
a = 1 - α = 2.
Now, eccentricity of the hyperbola is given by {Since
given}
Therefore, the equation of the given hyperbola will be
. (Answer)
Answer:
slope = -
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
2x + 3y = - 12 ( subtract 2x from both sides )
3y = - 2x - 12 ( divide all terms by 3 )
y = - x - 4 ← in slope- intercept form
with slope m = -
Answer:
(2, 2 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
[ (x₁ + x₂ ) ,
(y₁ + y₂ ) ]
Here (x₁, y₁ ) = (A(5, 8) and (x₂, y₂ ) = B(- 1, - 4) , thus
midpoint = [ (5 - 1),
(8 - 4 ) ] = (2, 2 )