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Find the value of k for which the line (k - 3) x - (4 - k 2) y + k 2 - 7k + 6 = 0 is
(a) Parallel to x-axis (b) Parallel to y-axis
(c) Passing through the origin
Solution:
The given equation of the line is
(k - 3)x - (4 - k2)y + k2 - 7k + 6 = 0 ....(1)
(a) Then given line can be written as
(k - 3)x + k2 - 7k + 6 = (4 - k2) y
y = (k - 3)/(4 - k2)x + (k2 - 7k + 6)/(4 - k2)
Which is of the form y = mx + c
Slope of the given line = (k - 3)/(4 - k2)
Slope of the x-axis = 0
If the given line is parallel to the x-axis then,
Slope of the given line = Slope of the x-axis.
⇒ (k - 3)/(4 - k2) = 0
⇒ k - 3 = 0
⇒ k = 3
Thus, the given line is parallel to x-axis, then the value of k = 3.
(b) If the given line is parallel to the y-axis, it is vertical.
Hence, its slope will be undefined.
The slope of the given line is = (k - 3)/(4 - k2)
Now, (k - 3)/(4 - k2) is defined at k2 = 4
⇒ k2 = 4
⇒ k = ± 2
Thus, if the given line is parallel to the y-axis, then the value of k = ± 2
(c) If the given line is passing through the origin, then point (0, 0) satisfies the given equation of the line.
(k - 3)(0) - (4 - k2)(0) + k2 - 7k + 6 = 0
⇒ k2 - 7k + 6 = 0
⇒ k2 - 6k - k + 6 = 0
⇒ (k - 6)(k - 1) = 0
⇒ k = 6 or k = 1
Thus, if the given line is passing through the origin, then the value of k is either 1 or 6
NCERT Solutions Class 11 Maths Chapter 10 Exercise ME Question 1
Find the value of k for which the line (k - 3) x - (4 - k 2) y + k 2 - 7k + 6 = 0 is (a) Parallel to x-axis (b) Parallel to y-axis (c) Passing through the origin.
Summary:
a) The given line is parallel to x-axis, then the value of k = 3
b) The given line is parallel to the y-axis, then the value of k = ± 2
c) The given line is passing through the origin, then the value of k is either 1 or 6
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