IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

waterdemon

Here is the solution:

The equation of the parabola is:
169 {(x-1)² + (y-3)² } = (5x - 12y + 17)²

Now this equation of the parabola can be given as:
(x-1)² + (y-3)² = { (5x - 12y + 17)/

(5)² + (12)² }²

This is nothing but form of:
SP = PM form
where S = Focus of parabola
and P = any point on parabola.
and M = perpendicular from point "P" to "Directrix".

Therefore,from above equation:
Focus S = (1,3) and directrix = 5x - 12y + 17 = 0
Therefore,
Let Z be the intercept of directrix and X-axis.
Then
SZ = perpenicular distance of focus S from directrix = 2a

SZ = 2a = 5-36+17/13 = 14/13 = 2a

Latus rectum = 4a
Latus Rectum = 2(2a)
Latus Rectum = 28/13.

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