Question

20p"y2° + 11py - 2 from 7p"y?° - py' +12​

Answer 1

Answer:

12x

2

+7xy−py

2

−18x+qy+6=0

represent pair of line when Δ=0

⇒

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

12

2

7

−9

2

7

−p

2

q

−9

2

q

6

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

∣

=0

⇒12(−6p−

4

q

2

)−

2

7

(21+

2

9q

)−9(

4

7q

−p9)=0 ...(1)

And represent pair of perpendicular lines when

12−p=0⇒p=12

Substituting this in (1) and solving we get

q=1,−

2

23

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