KVPY SX SB Exam 2013 Question Paper

Question : 83 of 120

Marks: +1, -0

The vertices of the base of an isosceles triangle lie on a parabola

y ^2 = 4x

and the base is a part of the line

y = 2x - 4

. If the third vertex of the triangle lies on the x-axis, its coordinates are

Solution:

(2x - 4)^2 = 4x

(x - 2)^2 = x

x^2- 5x + 4 = 0

C(1, -2)
B(4, 4) since AB = AC

√{(α-4)^2+16}=√{(α-1)^2+4}

On solving, we get

α=9/2

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