SOLUTION: Compute the focal length and the length of the latus rectum of the parabola y^2 + 8x

SOLUTION: Compute the focal length and the length of the latus rectum of the parabola y^2 + 8x - 6y + 25 = 0.

Question 512206: Compute the focal length and the length of the latus rectum of the parabola y^2 + 8x - 6y + 25 = 0.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Compute the focal length and the length of the latus rectum of the parabola y^2 + 8x - 6y + 25 = 0.
**
y^2+8x-6y+25=0
complete the square
(y^2-6y+9)+8x+25-9=0
(y-3)^2+8x+16=0
(y-3)^2+8(x+2)=0
(y-3)^2=-8(x+2)
this is an equation of a parabola of standard form: (y-k)^2=-4p(x-h)^2, with (h,k) being the (x,y) coordinates of the vertex
For given equation: (y-3)^2=-8(x+2)
vertex: (-2,3)
4p=8
p=2
latus rectum=focal width=4p=8
focal point:(-4,3)
focal length=distance from vertex to focal point on axis of symmetry=p=2
RELATED QUESTIONS
Find the latus rectum of given equation... (answered by josgarithmetic,stanbon)

Find the latus rectum, vertex and directrix of the parabola... (answered by MathLover1,josgarithmetic,MathTherapy)

Find the focus, vertex, length of latus rectum,and the equation of directrix of the... (answered by josgarithmetic,greenestamps)

PARABOLA: what's the vertex, focus, directrix, latus rectum and graph of the... (answered by solver91311)

Find the vertex, focus, length of latus rectum,and the equation of directrix of x^2 - 2x... (answered by josgarithmetic)

what is the length of the latus rectum of the parabola x^2-6x-2y-1=0? (answered by stanbon)

Given the parabola having the equation x^2+4y+8x=4, find the vertex, focus, and the... (answered by josgarithmetic)

Given the parabola having the equation x^2+4y+8x=-4, find the vertex, focus, and the... (answered by josgarithmetic)

What would be the length of latus rectum and vertex of the parabola... (answered by josgarithmetic)