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Analytical Geometry

Blazing goIITian

Joined:	14 Aug 2007
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5 Nov 2007 21:07:14 IST

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669

straight lines(tough questions)

None

1.if the slope of one of the line represented by ax²+2hxy+by²=0 be the square of the other,then prove that a+b/h + 8h²/ab = 6.

2.prove that the product of perpendiculars from (x₁,y₁) on the lines represented by ax²+2hxy+by²=0 is ax₁² + 2hx₁y₁ + by₁²/ root (a-b)² + 4h².

kindly help 5 points assured for one answer

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Comments (3)

Rohan

Blazing goIITian

Joined: 3 Jun 2007

Posts: 696

5 Nov 2007 22:02:29 IST

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question one can be easily solved by 2 formulas i.e.

m1 + m2 = -2h/b

and

m1.m2=a/b

given that if one slope is m then other is m^2

so

m+m^2=-2h/b
and
m^3=a/b

solve these eqns and u will get the answer
if not getting then tell me i will solve

and don't forget to rate me

Arshdeep Singh Malhan

Blazing goIITian

Joined: 14 Aug 2007

Posts: 910

6 Nov 2007 12:10:33 IST

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please solve the question for me.i will surely rate you.

venkat v.t

Scorching goIITian

Joined: 7 Aug 2007

Posts: 244

10 Nov 2007 14:25:53 IST

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2) Let the pair of lines be y=m₁x and y=m₂x.

use the perpendicular distace formula to both the lines from (x_1,y₁)

and multiply . Also m₁+m₂= -2h/b and m₁m₂= a/b,........(1)

we get

d= (m₁x₁-y₁)/square root(m₁²+1) . ( m₂x₁-y₁)/sqre root(m₂²+1)

= [m₁m₂ x²-x₁y₁(m₁+m₂)+y₁²]/root of [ (m₁m₂)²+m₁²+m₂²+1]

Now use equations (1) u will get the required answer

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