Question

If the straight lines represented by 9x^2 – 12xy + ky^2 = 0 be perpendicular to each other then find the value of k.
please answer it quickly..​

Answer 1

Answer:

ANSWER

5x

2

+12xy−6y

2

+4x−2y+3=0 ------ ( 1 )

x+ky−1=0

x+ky=1 ----- ( 2 )

Hamoginizing ( 1 ) with ( 2 )

⇒ 5x

2

+12xy−6y

2

+4x(x+ky)−2y(x+ky)+3(x+ky)

2

=0

⇒ 5x

2

+12xy−6y

2

+4x

2

+4kxy−2xy−2ky

2

+3(x

2

+kxy+k

2

y

2

)=0

⇒ 9x

2

+10xy−6y

2

+4kxy−2ky

2

+3x

2

+3kxy+3k

2

y

2

=0

⇒ 12x

2

+(10+4k+6k)xy+(3k

2

−2k−6)y

2

=0

⇒ 12x

2

+(10+10k)xy+(3k

2

−2k−6)y

2

=0

Pair of lines are equally inclined to the axes.

∴ Coefficient of xy=0

⇒ 10k+10=0

⇒ 10k=−10

⇒ k=−1

∴ ∣k∣=∣−1∣=1

Step-by-step explanation:

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