1.

Find the equations of axis and directrix of the parabola y2 + 6y – 2x + 5 = 0.

Answer»

y2 + 6y = 2x – 5 

Adding '9' on both sides we get, 

y2 + 6y + 9 = 2x – 5 + 9 

[y – (–3)]2 = 2x + 4 

[y – (–3)]2 = 2[x – (–2)] 

Comparing with (y – k)2 = 4a (x – h) we get, 

(h, k) = (–2, –3), a = (1/2) 

Equation of the axis y – k = 0 i.e. y + 3 = 0 

Equation of the directrix x – h + a = 0 

i.e., x – (–2) + (1/2) = 0 

2x + 5 = 0.



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