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ABCD is a square with side AB=2 .A point P moves such that its distance from A equals its distance from line BD.The locus of P meets the line AC at T 1 and the line through a parallel to BD at T 2 and T 3 . The area of triangle T 1 T 2 T 3 is...??? ​a)1/2 b)2/3 c)1 d)2

ABCD is a square with side AB=2 .A point P moves such that its distance from A equals its distance from line BD.The locus of P meets the line AC at T1 and the line through a  parallel to BD at T2  and T3 . The area of triangle T1T2T3 is...???
​a)1/2                         b)2/3
c)1                            d)2

Grade:12

1 Answers

Ravi
askIITians Faculty 69 Points
6 years ago
The locus of point P will be a parabola that is equidistant from A and BD(Focus and directrix). This meets line AC at T1. Line AC passes through the points (0,2) and (2,0). Use this information to find the equation of line using the intercept form of a line.(x+y=2). The point of intersection of locus of P: Parabola and the line AC will give T1. Similarily find the coordinates of T2 and T3 and use the determinant form to find the area of triangle.

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