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 x^2-2h x y-b y^2=0` `b x^2-2h x y+a y^2=0` `b x^2+2h x y+a y^2=0` `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

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

Find the value of a for which the lines represented by a x^2+5x y+2y^2=0 are mutually perpendicular.

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 Both the statements are true but statement 2 is the correct explanation of statement 1. Both the statements are true but statement 2 is not the correct explanation of statement 1. Statement 1 is true and statement 2 is false. Statement 1 is false and statement 2 is true.

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.

If the pairs of lines x^2+2x y+a y^2=0 and a x^2+2x y+y^2=0 have exactly one line in common, then the joint equation of the other two lines is given by (a) 3x^2+8x y-3y^2=0 (b) 3x^2+10 x y+3y^2=0 (c) y^2+2x y-3x^2=0 (d) x^2+2x y-3y^2=0

If the slope of one of the lines represented by a x^2+2h x y+b y^2=0 is the square of the other, then (a+b)/h+(8h^2)/(a b)= (a) 4 (b) 6 (c) 8 (d) none of these

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

If the gradient of one of the lines x^2+h x y+2y^2=0 is twice that of the other, then h=