Question

If one of the lines represented by \[a{x^2} + 2hxy + b{y^2} = 0\] is the Y-axis then the equation of the other line is
A) \[ax + 2hy = 0\]
B) \[2hx + by = 0\]
C) \[ax + by = 0\]
D) \[hx + by = 0\]

Answer 1

Hint: in this question, we have to find equation one of the line included in given equation. In order to find that we just rearrange the given equation and compare it with various standard equations like straight line, parabola and ellipse etc.



Formula Used:In this question we are going use the concept that equation of y axis is\[x = 0\]and trying to find the variables present in given equation and then put it in given equation and we will get required value.



Complete step by step solution:Given: \[a{x^2} + 2hxy + b{y^2} = 0\]
Now we know that equation of y axis is \[x = 0\]
Put this value in given equation.
\[a \times 0 + 2h \times 0y + b{y^2} = 0\]
Now we get
\[b = 0\]
After putting \[x = 0\]in given equation, equation becomes
\[a{x^2} + 2hxy = 0\]
\[x(ax + 2hy) = 0\]
Now required equation is
\[ax + 2hy = 0\]



Option ‘A’ is correct



Note: Here we have to remember that equation of y axis is\[x = 0\]
In this type of questions always follow the instruction given in the question to get required value easily foe example in this question it is given that one of the line in the given equation is y axis.
Don’t try to apply any formula related to any geometrical shape in this type of questions otherwise it becomes very complicated to get the solution.
Some standard equations are given as
Equation of straight lines
\[y = mx + c\]
Equation of parabola
\[{y^2} = 4ax\]
Equation of circle
\[{x^2} + {y^2} + 2gx + 2fy + c = 0\]
Equation of ellipse
             \[\dfrac{{{x^2}}}{{{a^2}}} + \dfrac{{{y^2}}}{{{b^2}}} = 1\]