The length of the latus rectum of the parabola y^2 + 8x -2y + 17 = 0
Answers
Given : y² + 8x -2y + 17 = 0
To find : length of the latus rectum of the parabola
Solution:
y² + 8x -2y + 17 = 0
=> ( y - 1)² - 1 + 8x + 17 = 0
=> ( y - 1)² + 8x + 16 = 0
=> ( y - 1)² = -8x - 16
=> ( y - 1)² = -8 (x + 2)
=> ( y - 1)² = 4(-2) (x + 2)
Comparing with
( y - k)² = 4p (x - h)
4p = -8
length of the Latus rectum = 8
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Step-by-step explanation:
Given The length of the latus rectum of the parabola y^2 + 8x -2y + 17 = 0
- So we will write the equation as
- So y^2 – 2y = - 8x – 17
- To make it a whole square we can write this as
- So y^2 – 2 x 1 x y + 1^2 = - 8x – 17 + 1^2
- So (y – 1)^2 = - 8x – 16
- (y – 1)^2 = - 8(x + 2)
- (y – 1)^2 = - 4 x 2 (x + 2)
- So Y^2 = - 4 a x. (so it will be a left parabola)
- Now comparing both equations we get a = 2
- Therefore length of latus rectum will be 4 a
- = 4 x 2
- = 8
Reference link will be
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