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Q.

In the given figure, a parabola is drawn to pass through the vertices B, C and D of the square are ABCD .If the coordinates of A and C are  (2,1) and (2,3), respectively, then focus of this parabola is

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a

(1,11/4)

b

(2,11/4)

c

(3,13/4)

d

(2,13/4)

answer is B.

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Detailed Solution

AC is parallel to y axis, its mid point is (2,2) .  Thus, B≡(3,2) and D≡(1,2) .  Equation of parabola is (x−2)2=λ(y−3) .  It passes through (3,2), so λ=−1 .  Thus, equation of parabola reduces to (x−2)2=−(y−3) .  Hence, axis is (x−2)2 and latus rectum line is y−3=−1/4 .  For focus, x−2=0 and y−3=−1/4 .  Therefore, focus is (2,11/4) .
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In the given figure, a parabola is drawn to pass through the vertices B, C and D of the square are ABCD .If the coordinates of A and C are  (2,1) and (2,3), respectively, then focus of this parabola is