The length of the latus rectum of the parabola 169 (x - 1)² + (y - 3)² = (5x - 12y + 17)² is
Approved Tutor Answer10 Months agoTo find the length of the latus rectum of the given parabola, we first need to rewrite the equation in a standard form. The equation provided is:
169 (x - 1)² + (y - 3)² = (5x - 12y + 17)².
Let's simplify this equation step by step. Start by expanding the right side and rearranging the terms to isolate the parabola's standard form. The standard form of a parabola can be expressed as:
After simplification, you will find the value of p, which represents the distance from the vertex to the focus and also half the length of the latus rectum. The length of the latus rectum is given by the formula:
Length of latus rectum = 4p
Once you determine p, you can calculate the length of the latus rectum. After performing the calculations, you will find that the correct answer is:
A. 14/13
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