conic sections- parabola vertex at origin has its focus at the centre of x2+y2-10x+9=0 find its directrix and latus rectum
Answers
Answer:
Directrix : x + 5 = 0
Latus Rectum ; 20
Step-by-step explanation:
Hi,
Given equation of circle is
x² + y² - 10x + 9 = 0
Center of circle = (-1/2*coefficient of x, -1/2*coefficient of y)
Center of the above circle is ( 5, 0).
For the given parabola,
Vertex is at Origin O (0, 0)
Focus is at the center of the circle , S ( 5, 0)
Axis of the parabola is the line joining the vertex and focus of parabola,
Since both the vertex and focus have their y-coordinate as 0
Equation of Axis is x-axis which is y = 0.
Distance between the Vertex and Focus is 'a' which is 1/4 th of Latus
Rectum
⇒1/4 * Latus Rectum = 5
⇒ Latus Rectum = 20.
Directrix is the line perpendicular to the axis and passing through the point
Z on the axis such that midpoint of SZ is the vertex of the parabola.
Hence , coordinates of Z will be ( -5, 0).
Any equal perpendicular to x-axis will be of the form x = k , but this passes
through Z( -5, 0),hence
Equation of directrix is x = -5.
Hope, it helps !
Answer:
Step-by-step explanation:
Given equation of circle is
x² + y² - 10x + 9 = 0
Center of circle = (-1/2*coefficient of x, -1/2*coefficient of y)
Center of the above circle is ( 5, 0).
For the given parabola,
Vertex is at Origin O (0, 0)
Focus is at the center of the circle , S ( 5, 0)
The equation of directrix is x+5=0
Then directrix is -5
Lrngth of latus rectum is 4a where a is 5
Length of latus rectum is 20
THANK YOU.