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Describe, sketch and label the focus, vortex and
directrix of the Parabola
4y2 + 8y - 8x +7=0
Answers
Given : 4y² + 8y - 8x +7=0
To Find : sketch and label the focus, vertex and directrix of the Parabola
Solution:
4y² + 8y - 8x +7=0
=> 4y² + 8y + 4 - 4 - 8x + 7 = 0
=> 4(y² + 2y + 1) -8x +3 = 0
=> 4(y + 1)² - 8x + 3 = 0
=> 4(y + 1)² = 8x - 3
=> (y + 1)² = 2x - 3/4
=> (y + 1)² = 2( x - 3/8)
=> (y + 1)² = 4(1/2)( x - 3/8)
comparing with (y - k)² = 4p(x - h)
h = 3/8 , k= - 1 , p = 1/2
Vertex ( h , k) = ( 3/8 , -1)
The directrix is the line x = h - p. = 3/8 - 1/2 = -1/8
directrix , x = -1/8
The focus is at (h + p, k) = (3/8 + 1/2 , -1) = (7/8 , -1)
Axis of symmetry is y = - 1
Horizontal parabola opening toward +ve x axis.
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