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NDA 2025 Maths · Mathematics · Conic Sections · medium

The focus of the parabola x^2-6x-4y+17=0 is

Single correct option

The focus of the parabola x2−6x−4y+17=0x^2-6x-4y+17=0 is
  1. A. (3,2)(3,2)
  2. B. (4,2)(4,2)
  3. C. (3,1)(3,1)
  4. D. (3,3)(3,3)
Show answer and solution

Answer: (D) (3,3)(3,3)

Rewrite as (x−3)2=4y−8=4(y−2)(x-3)^2=4y-8=4(y-2). This is X2=4aYX^2=4aY with a=1a=1, X=x−3X=x-3, Y=y−2Y=y-2, so the vertex is (3,2)(3,2) and the focus is a=1a=1 above it, at (3,3)(3,3). The option (3,2)(3,2) is the vertex, (3,1)(3,1) is the point below the vertex, and (4,2)(4,2) moves along the wrong axis.
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