The correct option is C All of the above
Detailed step-by-step solution:
Since both the lines pass through the origin, the equation of the lines is in the form of y=mx.
Let the equation of the first line be y=m1x, and the equation of the second line be y=m2x.
Slope of the first line: y=m1x
slope =m1 (slope = m in the equation y=mx)
Slope of the second line: y=m2x
slope =m2 (slope = m in the equation y=mx)
(Slope of the first line) + (Slope of the second line) =0
⇒ m1+m2=0
⇒ m2=−m1
Let m1=m.
⇒ m2=−m
Equation of the first line: y=mx
Equation of the second line: y=−mx
Line 1 passes through (a,4).
4=am (substituting x=a and y=4 in y=mx)
⇒ a=4m
⇒ b=−m(−3) (substituting x=−3 and y=b in y=−mx)
⇒ b=3m
Multiplying a and b, we get:
a×b=4m×(3m)
⇒ ab=12
Let’s check the options.
A. a=2,b=6: Substituting in ab=12, we get:
2×6=12
2 and 6 can be the values of a and b, respectively.
B. a=4,b=3: Substituting in ab=12, we get:
4×3=12
4 and 3 can be the values of a and b, respectively.
C. a=−3,b=−4: Substituting in ab=12, we get:
(−3)×(−4)=12
−3 and −4 can be the values of a and b, respectively.
Option D is correct.