Math, asked by rishikakasturi, 4 months ago

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

Answered by amitnrw
2

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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