Question

Find the axis, vertex, focus, equation
of directrix and the length of latus rectum
for the parabola x2+ 6x – 4y + 21 = 0​

Answer 1

Answer:

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Explanation:

Given y

2

=−12x

Since the above equation is involving y

2

Its axis is x−axis

Also coefficient of x is negative (-12)

Hence we use equation

y

2

=−4ax

Comparing

y

2

=−12x....(1) [Given]

y

2

=−4ax

From (1) and (2)

−12x=−4ax

4ax=12x

a=3

Coordinates of focus is (-a,0)

i.e focus (−3,0)

Equation of directix is

x=a

x=3

Latus rectum =4a

=4×3

=12