Question

The triangle formed by x + 3y
1 and 9x² -12xy + ky² = 0 is
right angled triangle and
kis not equal to 9. Then k =
(A) 3 (B) 5 (C) 7 (D) 1​

Answer 1

Answer:

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Step-by-step explanation:

if we see,

x+3y ± 1

and

9x^2 - 12xy +ky^2

they both add up to zero

and they are forming right angled triangle

and k ≠ 9

so , by pythagoras thm.

(x+3y ± 1)^2 + (9x^2 - 12xy +ky^2)^2 = 0^2( since they add to zero , so they will add up to zero now also)

so,

on simplifying,

x^2 + 9y^2 +1 + 6xy ± 6y ± 2x = -( 81x^4 - 144x^2y^2 + k^2y^4 - 216x^3y - 24kxy^3 +18kx^2y^2)

now you simplify to get the answer