Question 24.
Find the length of the latus rectum of the parabola
169 [(x - 1)^2 + (y - 3)^2] = (5x - 12y + 17)^2.
Answer 24.
(x - 1)^2 + (y - 3)^2 is square of the distance from any point (x, y) to (1, 3)
(5x - 12y + 17)^2 / 169 is square of the distance of the point (x, y) from the line 5x - 12y + 17 = 0
As both are equal, according to the definition of the parabola, the given equation is a parabola whose focus is S(1, 3) and directrix is 5x - 12y + 17 = 0.
A line through the focus and parallel to the directrix is the latus rectum.
Let A and B be the end-points of the latus rectum.
Distance from A to S = distance from A to the directrix = l 5*1 - 12*3 + 17l / √(5^2 + 12^2) = 14/13
Length of latus rectum = AB = 2 AS = 2 * (14/13) = 28/13.
Link to YA!
Find the length of the latus rectum of the parabola
169 [(x - 1)^2 + (y - 3)^2] = (5x - 12y + 17)^2.
Answer 24.
(x - 1)^2 + (y - 3)^2 is square of the distance from any point (x, y) to (1, 3)
(5x - 12y + 17)^2 / 169 is square of the distance of the point (x, y) from the line 5x - 12y + 17 = 0
As both are equal, according to the definition of the parabola, the given equation is a parabola whose focus is S(1, 3) and directrix is 5x - 12y + 17 = 0.
A line through the focus and parallel to the directrix is the latus rectum.
Let A and B be the end-points of the latus rectum.
Distance from A to S = distance from A to the directrix = l 5*1 - 12*3 + 17l / √(5^2 + 12^2) = 14/13
Length of latus rectum = AB = 2 AS = 2 * (14/13) = 28/13.
Link to YA!
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