16. The triangle formed by x + 3y = 1
and 9x2–12xy + ky2 = 0 is right angled
triangle and k + -9. Then k =
3
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Answers
Answered by
2
Answer:
Correct option is
A
3
x+3y=1
Slope =
3
−1
9x
2
−12xy+ky
2
=0−−−−(1)
Let y=m
1
x and y=m
2
x are two straight lines of
(y−m
1
x)(y−m
2
x)=0
y
2
−(m
1
+m
2
)xy+m
1
m
2
x
2
=0 ---(2)
As given x+3y=1 formed right angle with one of the line
9x
2
−12xy+ky
2
=0
So, let,
m
1
=3
So, compare 1) & 2)
m
1
+m
2
=
k
12
⇒m
2
+3=
k
12
m
1
m
2
=
k
9
⇒m
2
=
k
3
⇒
k
3
+3=
k
12
⇒3=
k
9
⇒k=3
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