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Passage: For the parabola y2 = 4ax, the vertex is (0, 0), the focus is (a, 0) and the directrix is x + a = 0.
Answer the following three questions.
(i) The vertex of the parabola (y – 1)2 = 2(x – 1) is
(A) (1,0)
(B) (2,0)
(C) (1,1)
(D) (0,1)
(ii) Focus of the parabola y2 = 4(x – 1) is
(A) (1, 0)
(B) (2, 0)
(C) (1, 1)
(D) (2, 2)
(iii) The directrix of the parabola (y – 2)2 = 4(x – 1)
(A) x = 1
(B) x = -1
(C) x = 2
(D) x = 0
Passage: For the parabola y2 = 4ax, the vertex is (0, 0), the focus is (a, 0) and the directrix is x + a = 0.
Answer the following three questions.
(i) The vertex of the parabola (y – 1)2 = 2(x – 1) is
(A) (1,0)
(B) (2,0)
(C) (1,1)
(D) (0,1)
(ii) Focus of the parabola y2 = 4(x – 1) is
(A) (1, 0)
(B) (2, 0)
(C) (1, 1)
(D) (2, 2)
(iii) The directrix of the parabola (y – 2)2 = 4(x – 1)
(A) x = 1
(B) x = -1
(C) x = 2
(D) x = 0
Correct option (i)(c)(ii)(b)(iii)(d)
Explanation :
(i) The parabola is
Y2 = 4(1/2)(x)
where X = x – 1 and Y = y – 1. Therefore, the vertex is
(X = 0, Y = 0) = (x – 1 = 0, y – 1 = 0) = (1, 1)
(ii) y2 = 4(x -1) is Y2 = 4X where X = x – 1 and Y = y and a – 1. The focus is
(X = 1, Y = 0) =(x – 1 = 1,y = 0) = (2,0)
(iii) (y – 2)2 = 4(x – 1) ⇒ Y2 = 4X where X = x – 1 and Y = y − 2. The directrix equation is
X = -a = -1
⇒ x – 1 = -1
⇒ x = 0