IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

vsraghuvar

	Two lines represented by the equation x² - y² - 2x + 1 = 0 are rotated about the point (1, 0), the line making the bigger angle with the positive directionof the x-axis being turned by 45^o in the clockwise sense and the other line being turned by 15^o in the anticlockwise sense. The combined equation of the pair of lines in their new position is

	1.

	2.

	3.

	4.	none of these

Decoder

first of all see wat r the lines..

they r .. x - y - 1.. and x+y-1..

we observe tht both pass through (1,0)..so rotation is not a problem...

second line is making bigger angle..( 135) ..if we turn it ..it gets to 90...the line becomes nothing but x=1..

now the first line..
after rotation it is a line with angle ( 45 + 15) ...passing through pt. 1,0..

so line is y = root3 (x-1)..

multiply both eq.
u get

(x-1)( y - root3x + root3)..

solve now u get..

1 as correct...

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