Pair Of Straight Lines Question 152
Question: The equation $ {{(x-5)}^{2}}+(x-5)(y-6)-2{{(y-6)}^{2}}=0 $ represents
Options:
A) A circle
B) Two straight lines passing through origin
C) Two straight lines passing through the point (5, 6)
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ {{(x-5)}^{2}}+(x-5)(y-6)-2{{(y-6)}^{2}}=0 $
Therefore $ x^{2}+25-10x+xy+30-6x-5y-2y^{2}-72+24y=0 $
$ \Rightarrow x^{2}+xy-2y^{2}-16x+19y-17=0 $
Obviously, it is not a circle as $ a\ne b $ and xy is present.
On checking for pair of straight lines, we get that the equation represents a pair of straight lines.
Also for $ x=5,\ y=6, $ equation vanishes. Therefore it passes through (5, 6).
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