Necesito la solución de estos dos ejercicios. Por favor
(No hace falta hacer la gráfica sólo necesito lo demás)
Answers
Answer:
Step-by-step explanation:
Given : x² - 4x + 3 - y = 0 , 3x² - 6x + 5 + y = 0
To find : Vertex , Directrix & Focus
Solution:
equation of a parabola
(x - h)² = 4p(y - k) where
(h,k) are the coordinates of the vertex.
directrix y = k - p
focus ( h , k + p)
x² - 4x + 3 - y = 0
=> (x - 2)² - 4 + 3 - y = 0
=> (x - 2)² = y + 1
=> (x - 2)² = 4(1/4)(y -(-1))
h = 2 , k = - 1 p = 1/4
Vertex = ( 2 , - 1)
directrix = -1 - 1/4 = -5/4
focus = ( 2 , -3/4)
3x² - 6x + 5 + y = 0
=> x² - 2x + 5/3 + y/3 = 0
=> (x - 1)² - 1 + 5/3 + y/3= 0
=> (x - 1)² = -(1/3)(y + 2)
=> (x - 1)² = 4(-1/12)(y -(-2))
h =1 , k = - 2 p = -1/12
Vertex = ( 1 , - 2)
directrix = -2+ 1/12 = -23/12
focus = ( 1 , -25/12)
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