6. If the co–ordinates of centroid of  Δ ABC  with  A (4, 2), B (2, 2a) and C (0, 2) are equal, then find the value of  a.

 Soln. Centroid G  =      =   

= 

But we are  given that,   2   =    ⇒   a  =  1

7. A(1, 4), B(9 – 12) and P (6, –6), then P divides from A in the ratio ……….. .

Soln. A (x₁, y₁) & B ( x₂, y₂). If  P (x, y) divides  from A in the ratio λ = m : n, then

          and       

 ∴  6     = 

∴  5n  =  3m – 6    = 

∴  5n  =  3m

 ∴ 

8. If the parametric equation of AB   are  x  =  – 7t + 3 and y = 7t – 3, t ∈ R. Then, the cartesian equation is  ………………

Soln. Here, x  =  – 7t  +  3  ⇒  7t  =  3 – x, then from y = 7t – 3,

By elimination method, the cartesian equation is :  x + y  =  0.

9. A(0, 0), B(a, 2), C(0, – 1) and D ( 1, – 3). And AB  ⊥ CD,  then find a.

Soln. Slope of  AB  =  m₁  = 

&   Slope of  CD  =  m₂  = 

 ow,  AB  ⊥ CD

⇒  m₁ ∙ m₂ =   – 1

⇒  =   – 1

⇒   a   =   4

10. If lines x + y + μ =  0  and  λx – 5y  =  5  are coincident, then find μ + λ.

Soln. Since lines  x + y + μ =  0  and  λx – 5y  –  5   =  0  are coincident,

then,   ⇒ 

⇒    λ  =   – 5  &   μ = 1    ⇒    μ + λ = – 4

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