## Question

The equation represents a The Pair of Straight Lines passing through the origin. The two lines are

### Solution

Real and distinct if *h*^{2} > 9

The equation *ax*^{2} + 2*hxy* + *by*^{2} = 0 represents a pair of real and distinct lines if *h*^{2} > *ab*. The given equation will represent a pair of real and distinct lines if *h*^{2} > 9. [âˆµ *a* = 3, *b* = 3]

#### SIMILAR QUESTIONS

If the equation represents two straight lines, then the product from the origin on these straight lines, is

If represents two parallel straight lines, then

If represents two parallel lines, then the distance between them is

The equation of pair of lines joining origin to the points of intersection of*x*^{2} + *y*^{2} = 9 and *x *+ *y* =3, is

The tangent to the angle between the lines joining the origin to the points of intersection of the line y = 3x + 2 and the curve *x*^{2} + 2*xy* + 3*y*^{2} + 4*x* + 8*y* – 11 = 0, is

The angle between the lines joining the origin to the point of intersection of the line and the circle *x*^{2} + *y*^{2} = 4, is

The straight lines joining the origin to the points of intersection of the line*kx* + *hy* = 2*hk* with the curve (*x* – *h*)^{2} + (*y* – *k*)^{2} = *c*^{2} are at right angles, if

If the lines joining the origin to the points of intersection of the line *y* = *mx*+ 2 and the curve *x*^{2} + *y*^{2} = 1 are at right-angles, then

The equation represents a The Pair of Straight Lines, if

If the pairs of straight lines *ax*^{2} + 2*hxy* – *ay*^{2} = 0 and *bx*^{2} + 2*gxy* – *by*^{2} = 0 be such that each bisects the angles between the other, then