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Family of Lines - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Family of Lines is considered one of the most asked concept.

  • 21 Questions around this concept.

Solve by difficulty

QuestionMEDIUM

If the lines 3y + 4x = 1, y = x + 5 and 5y + bx = 3 are concurrent, then the value of b is

 

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A line which makes an acute angle \mathrm{\theta } with the positive direction of the \mathrm{ x-axis } is drawn through the point \mathrm{ P(3, 4) }, to cut the curve \mathrm{ y^2 = 4x} at \mathrm{ Q}  and \mathrm{R}. The lengths of the segments \mathrm{PQ}  and \mathrm{PR} are numerical values of the roots of the equation \mathrm{r2} \mathrm{sin2} \mathrm{\theta }  \mathrm{ + 4r } \mathrm{\left ( 2 sin \theta - cos \theta \right )} \mathrm{+ c } \mathrm{= 0, } where \mathrm{c = }

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If \mathrm{4 a^2+9 b^2-c^2+12 a b=0}, the family of straight lines \mathrm{a x+b y+c=0} is either concurrent at

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If \mathrm{a, b, c} are in H.P. then the straight line \mathrm{\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0} passes through a point, that point is

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Consider a family of straight lines \mathrm{(x+y)+\lambda(2 x-y+1)=0}. The equation of the straight line belonging to this family that is the farthest form (1,-3) is

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Concepts Covered - 0

Family of Lines

Family of Lines

Any equation of line through the point of intersection of the lines  \mathrm{L}_{1}=\mathrm{a}_{1} \mathrm{x}+\mathrm{b}_{1} \mathrm{y}+\mathrm{c}_{1}=0  and  \mathrm{L}_{2}=\mathrm{a}_{2} \mathrm{x}+\mathrm{b}_{2} \mathrm{y}+\mathrm{c}_{2}=0 can be represented as

\\ \mathrm{a}_{1} \mathrm{x}+\mathrm{b}_{1} \mathrm{y}+\mathrm{c}_{1}+\lambda\left(\mathrm{a}_{2} \mathrm{x}+\mathrm{b}_{2} \mathrm{y}+\mathrm{c}_{2}\right)=0 \\ \mathrm{or},\; \mathrm{L}_{1}+\lambda \mathrm{L}_{2}=0

Where λ is a parameter.

 

 

Note:.

  • The equation L1 + λL2 = 0 or μL1 + νL2 = 0  represents a line passing through the intersection of the lines L1 = 0 and L2 = 0 which is a fixed point. And λ,  μ , ν are constants.

Study other Related Concepts

Family of Lines Current Topic

Coordinate Axes
Distance Between Two Points Formula
Section Formula & Conic Sections
Centroid, Incentre and Circumcentre and Orthocentre of a Triangle
Excenters of Triangle
Circumcentre and Orthocentre
Incentre
Area of Triangle in Coordinate Geometry
Locus
Transformations of Axes

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