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Question

The equation of two equal sides of an isosceles triangle are 7xy+3=0 and x+y3=0. If the third side passes through (1,10) and its slope is negative, then the equation of the third side is
  1. 3x+y+7=0
  2. 2x+y+8=0
  3. 3x+y7=0
  4. x3y31=0


Solution

The correct option is A 3x+y+7=0
Let m be the slope of the third line.
Equation of the line with slope m and passing through (1,10) is
y+10=m(x1)
Since the third line makes equal angle with the given two lines,
m71+7m=m(1)1m
Taking positive signs, we get
m2+1=0 (Not possible)

Hence, m71+7m=(m+11m)
3m2+8m3=0
(3m1)(m+3)=0
m=13 or m=3
But m<0
Equation of the third line is 3x+y+7=0

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