find the equations of the axisand directrix of parabola ysquare+6y_2x+5=0 - Maths - Conic Sections

Question

find the equations of the axisand directrix of parabola
ysquare+6y_2x+5=0

Lalit Mehra · Accepted Answer

The equation of the parabola is y2+6y-2x+5=0
y2+6y-2x+5=0⇒y2+6y + 9 = 2x-5+9⇒y+32=2x+2Putting y + 3 =Y and x + 2 =X, we getY2=2XHere, 4a = 2⇒a=12Equation of the axis is Y=0 i
e  y + 3 = 0 or y = -3
Equation of the directrix is X=-12⇒x+2=-12 or x=-52