Q1.Sh o w that the line given by (2+k) x +(3-k) y= 7 + 6k for differ ent value of k,pa ss thro ugh a fix ed poi nt. Fin d the co- ordinates of the fixed poin t.
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Step-by-step explanation:
Given line,
⇒ (2 + k) x + ( 3 - k) y = 7 + 6k
⇒ 2x + kx + 3y - ky - 7 - 6k = 0
⇒ 1 ( 2x + 3y - 7) + k ( x - y - 6) = 0
This is of the form,
So the line represents two lines which intersect at a point. Therefore, For any value of k, The line passes through a fixed point.
Now, The fixed point is the point of intersection of the lines,
Solving the lines,
2x + 3y - 7 = 0
2x - 2y - 12 = 0
Adding them gives,
y - 19 = 0
y = 19
Finding the value of x,
x - 19 - 6 = 0
x - 25 = 0
x = 25.
Therefore, The fixed point is (25, 19).
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