The image of the pair of lines represented by `a x^2+2h x y+b y^2=0` by the line mirror `y=0` is a. `a x^2-2h x y-b y^2=0` b. `b x^2-2h x y+a y^2=0` c. `x^2+2h x y+a y^2=0` d. `a x^2-2h x y+b y^2=0`

A pair of perpendicular straight lines is drawn through the origin forming with the line 2x+3y=6 an isosceles triangle right-angled at the origin. The equation to the line pair is a. 5x^2-24 x y-5y^2=0 b. 5x^2-26 x y-5y^2=0 c. 5x^2+24 x y-5y^2=0 d. 5x^2+26 x y-5y^2=0

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

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2

Statement 1 : If -2h=a+b , then one line of the pair of lines a x^2+2h x y+b y^2=0 bisects the angle between the coordinate axes in the positive quadrant. Statement 2 : If a x+y(2h+a)=0 is a factor of a x^2+2h x y+b y^2=0, then b+2h+a=0 .

The straight lines represented by the equation 135 x^2-136 x y+33 y^2=0 are equally inclined to the line (a) x-2y=7 (b) x+2y=7 (c) x-2y=4 (d) 3x+2y=4

Show that the equation of the pair of lines bisecting the angles between the pair of bisectors of the angles between the pair of lines a x^2+2h x y+b y^2=0 is (a-b)(x^2-y^2)+4h x y=0.

The product of the perpendiculars from origin to the pair of lines a x^2+2h x y+b y^2 + 2gx + 2fy + c =0 is

If one of the lines denoted by the line pair a x^2+2h x y+b y^2=0 bisects the angle between the coordinate axes, then prove that (a+b)^2=4h^2

Find the combined equation of the pair of lines through the point (1, 0) and parallel to the lines represented by 2x^2-x y-y^2=0

Show that the pairs of straight lines 2x^2+6x y+y^2=0 and 4x^2+18 x y+y^2=0 are equally inclined