Given the equation of two straight lines passing through `(-5,13).` How many such lines are there?

Options

A. `" Infinite line"`
B. `" one line"`
C. `" Three lines"`
D. `" Four lines"`

Explanation

Let the equation of straight line be
ax + by =c
It passes through (-5,13)
`therefore` , a(-5)+b(13)=c
`rArr` , -5a+13b=c
Now wse can take any arbitrary values of a and b to get c:
Let , a==0 and b =1 `rArr` c=13
Putting these values of a,b and c in (1) we get
0.cx+1.y=13 `rArr` y=13
Let , a=4,b=2 `rArr` c=6
putting these values of a,b and c in eq (1) we get
4x+2y =6 `rArr` 2x+y=13
In the same manner we can get so many equations
Hence, there may be infinitely many lines (equations) passing through (-5,13).