SOLUTION: Find the focus, vertex, length of latus rectum,and the equation of directrix of the parabola y^2 - 10x = 0
Algebra.Com
Question 1119528: Find the focus, vertex, length of latus rectum,and the equation of directrix of the parabola y^2 - 10x = 0
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Vertex is (0,0).
-
Focus is ( 2.5, 0 ).
Directrix is .
--
-
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The equation has a y^2 term, so the parabola opens right or left. Vertex form for the equation of a parabola that opens right or left is
where the vertex is (h,k) and p is the directed distance from the directrix to the vertex and from the vertex to the focus.
Note with this form of the equation, the length of the latus rectum (perpendicular to the axis of symmetry and through the focus) is |4p|.
Put the given equation in that form:
This is in vertex form. The vertex is (0,0); p = 10/4 = 2.5.
vertex: (0,0)
focus: p = 2.5 right of the vertex, at (2.5,0)
directrix: p = 2.5 left of the vertex; x = -2.5
length of latus rectum: 4p = 10
RELATED QUESTIONS
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 y^2 - 4y... (answered by josgarithmetic,greenestamps)
Given the equation of the parabola (x+2)^2=2(y-1), find the vertex, directrix, focus and... (answered by josgarithmetic)
Find the vertex, focus, length of latus rectum,and the equation of directrix of x^2 - 2x... (answered by josgarithmetic)
Find the latus rectum, vertex and directrix of the parabola... (answered by MathLover1,josgarithmetic,MathTherapy)
Find the length of the latus rectum and the equation of the parabola with vertex at the... (answered by CPhill)
Find the vertex, focus, length of latus rectum and the equation of directrix from the... (answered by josgarithmetic)
Find the focus, vertex, directrix , axis, and latus rectum of the parabola, y2 =8x-8y (answered by lwsshak3)
How do I find the vertex, focus, directrix, axis of symmetry,
and latus rectum of this... (answered by Edwin McCravy)