Answer:
(2, - 6 )
Step-by-step explanation:
Given the 2 equations
x = y + 5 → (1)
2x + 3y = - 14 → (2)
Substitute x = y + 5 into (2)
2( y + 5 ) + 3y = - 14 ← distribute and simplify left side
y + 10 + 3y = - 14
4y + 10 = - 14 ( subtract 10 from both sides )
4y = - 24 ( divide both sides by 4 )
y = - 6
Substitute y = - 6 into (1) for corresponding value of x
x = (0.5 × - 6 ) + 5 = - 3 + 5 = 2
Solution is (2, - 6 )
Answer:
Step-by-step explanation:
A hyperbola is the locus of a point such that its distance from a point to two points (known as foci) is a positive constant.
The standard equation of a hyperbola centered at the origin with transverse on the x axis is given as:
The coordinates of the foci is at (±c, 0), where c² = a² + b²
Given that a hyperbola centered at the origin with x-intercepts +/- 4 and foci of +/-2√5. Since the x intercept is ±4, this means that at y = 0, x = 4. Substituting in the standard equation:
The foci c is at +/-2√5, using c² = a² + b²:
Substituting the value of a and b to get the equation of the hyperbola: