Math, asked by Anonymous, 1 year ago

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

Answered by VEDULAKRISHNACHAITAN
19

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 !

Answered by ezaetdestroyer
5

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.

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