The vertex and focus of the parabola 4y2 + 12x - 20y + 67 = 0 are (h, k) and (a, b) respectively then k-h+ b - 4a is
Answers
Given : 4y² + 12x - 20y + 67 = 0 vertex and focus of the parabola 4y² + 12x - 20y + 67 = 0 are (h, k) and (a, b)
To Find : k-h+ b - 4a
Solution:
4y² + 12x - 20y + 67 = 0
=> 12x = -4y²+ 20y - 67
=> 12x =-4(y² -5y) - 67
=> 12x = -4(y² -5y + 25/4 - 25/4) + 67
=> 12x = -4(y - 5/2)² + 25 - 67
=> 12x = -4(y - 5/2)² - 42
=> x = - (1/3)(y - 5/2)² - 42/12
=> x = - (1/3)(y - 5/2)² -7/2
x = a(y - k)² + h
a = -1/3
k = 5/2 ,h = -7/2
Focus ( h + 1/4a , k)
-7/2 + 1/4(-1/3) = -7/2 - 3/4 = -17/4
Focus ( -17/4 , 5/2)
k-h+ b - 4a
= 5/2 -(-7/2) + 5/2 - 4(-17/4 )
= 5/2 + 7/2 + 5/2 + 17
= 51/2
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