First slide

Parabola

Question

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

Moderate

A

$(1, 11 / 4)$
B

$(2, 11 / 4)$
C

$(3, 13 / 4)$
D

$(2, 13 / 4)$

Solution

$A C is parallel to y axis, its mid point is (2, 2) .$
$Thus, B \equiv (3, 2) and D \equiv (1, 2) .$
$Equation of parabola is (x - 2)^{2} = λ (y - 3) .$
$It passes through (3, 2), so λ = - 1 .$
$Thus, equation of parabola reduces to (x - 2)^{2} = - (y - 3) .$
$Hence, axis is (x - 2)^{2} and latus rectum line is y - 3 = - 1 / 4 .$
$For focus, x - 2 = 0 and y - 3 = - 1 / 4 .$
$Therefore, focus is (2, 11 / 4) .$

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