Two pairs of straight lines have the equations `y^(2)+xy-12x^(2)=0andax^(2)+2hxy+by^(2)=0`. One line will be common among them if

Question

Two pairs of straight lines have the equations `y^(2)+xy-12x^(2)=0andax^(2)+2hxy+by^(2)=0`. One line will be common among them if

Two pairs of straight lines have the equations `y^(2)+xy-12x^(2)=0andax^(2)+2hxy+by^(2)=0`. One line will be common among them if
A. `a+8h-16b=0`
B. `a-8h+16b=0`
C. `a-6h+9b=0`
D. `a+6h+9b=0`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

Related Questions

Prove that the straight lines joining the origin to the points of intersection of the straight line `hx+ky=2hk` and the curve `(x-k)^(2)+(y-h)^(2)=c^(

2 Answers 6 Views

If the pairs of lines `x^(2)+2xy+ay^(2)=0andax^(2)+2xy+y^(2)=0` have exactly one line in common then the joint equation of the other two lines is give

2 Answers 4 Views

The equations of a line which is parallel to the line common to the pair of lines given by `6x^(2)-xy-12y^(2)=0and15x^(2)+14xy-8y^(2)=0`and at a dista

2 Answers 5 Views

The equation `a^2x^2+2h(a+b)x y+b^2y^2=0` and `a x^2+2h x y+b y^2=0` represent two pairs of perpendicular straight lines two pairs of parallel straigh

2 Answers 5 Views

The image of the pair of lines represented by `ax^(2)+2hxy+by^(2)=0`by the line mirror `y=0` is

2 Answers 4 Views

If the slope of one of the lines represented by `ax^(2)+2hxy+by^(2)=0` is the square of the other , then `(a+b)/(h)+(8h^(2))/(ab)=`

2 Answers 4 Views

A particle straight line passes through orgin and a point whose abscissa is double of ordinate of the point. The equation of such straight line is :

2 Answers 5 Views

A line intersects the straight lines `5x-y-4=0` and `3x-4y-4=0` at `A` and `B` , respectively. If a point `P(1,5)` on the line `A B` is such that `A P

2 Answers 5 Views

A set of parallel chords of the parabola `y^2=4a x` have their midpoint on any straight line through the vertex any straight line through the focus a

2 Answers 4 Views

Consider quadratic equations `x^2-ax+b=0 and x^2+px+q=0` If the above equations have one common root and the other roots are reciprocals of each other

2 Answers 5 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 2,4
The equation `y^(2)+xy-12x^(2)=0` can be rewritten as
`(y+4x)(y-3x)=0`
or `(y)/(x)=-4,3`
The two pairs will have a line common if -4 or 3 is a root of
`b((y)/(x))^(2)+2h((y)/(x))+a=0`
`:. 9b+6h+a=0or16b-8h+a=0`

4 views Answered 2023-02-05 15:29