Distinguishing between Conics from General Equation and Eccentricity
The locus rep...
Question
The locus represented by the equation x2+y2−2x−2y+2=(2x+y−3)2 is
A
an ellipse
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B
a circle
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C
a pair of straight lines
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D
a hyperbola
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Solution
The correct option is C a pair of straight lines (x−1)2+(y−1)2=(2x+y−3)2
Comparing and making it in form of PS=e(PM) ⇒(x−1)2+(y−1)2=5(2x+y−3√5)2 ∴ Fixed point is (1,1) and
Fixed line is 2x+y−3=0
But (1,1) lies on given line. ∴ Pair of straight lines