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Analytical Geometry

Scorching goIITian

Joined:	28 Oct 2007
Post:	207

29 Oct 2007 20:38:31 IST

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378

An extremely tough circles and straight line question from AITS..

None

Q. The pair of straight lines joining the origin to the common points x² + y² =4 and y=3x+c are perpendicular if c² = ..........
a)20 b)13 c)1/5 d)5

Q. If a+b+3c=0, c not equal to zero and p and q be the real roots of the equation ax+bx+c=0 belonging to the set (0,1) and not belonging to the set (0,1) respectively,then locus of the point of intersection of lines
xcos@ + ysin@ =p and xcos@ -- ysin@=q where @is a parameter is :
a)a circle of radius 2 b) straight line c)parabola d)circle of radius 2.

Please help me out with these two questions..

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sowjanya gudipati

Cool goIITian

Joined: 13 Oct 2007

Posts: 75

30 Oct 2007 15:22:00 IST

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Q1)

first solve both the equations to get point of intersections which are

(-3c+(40-c²)^1/2/10 , c+3(40-c²)^1/2/10)

(-3c-(40-c²)^1/2/10 , c-3(40-c²)^1/2/10)

then for slope of line given two points on it will be

y₂-y₁/x₂-x₁

therefore m₁=c+3(40-c²)^1/2/-3c+(40-c²)^1/2

m₂=c-3(40-c²)^1/2/-3c-(40-c²)^1/2

use m₁xm₂=-1

then it gives equqtion in c²which is equal to 20

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