Prove that the equation `2x^(2)+5xy+3y^(2)+6x+7y+4=0` respresents a pair of straight lines .Find the coordinates of their point of intersection and also the angle between them.

Prove that the equation 2x^2+5x y+3y^2+6x+7y+4=0 represents a pair of straight lines. Find the coordinates of their point of intersection and also the angle between them.

If the equation 2x^(2)+2hxy +6y^(2) - 4x +5y -6 = 0 represents a pair of straight lines, then the length of intercept on the x-axis cut by the lines is equal to

If x^2-3xy+lambda y^2+3x-5y+2=0 ,represent a pair of straight lines, then the value of lambda is

If theta is the angle between the lines given by the equation 6x^2+5x y-4y^2+7x+13 y-3=0 , then find the equation of the line passing through the point of intersection of these lines and making an angle theta with the positive x-axis.

The equation of second degree x^2 + 2sqrt2 xy + 2y^2 + 4x + 4 sqrt2 y + 1 = 0 represents a pair of straight lines, the distance between them is :

Find the angle between the straight lines joining the origin to the point of intersection of 3x^2+5x y-3y^2+2x+3y=0 and 3x-2y=1

Find the equation of a straight line passing through the origin and through the point of intersection of the lines 5x + 7y =3 and 2x – 3y = 7

The angle between the lines joining the origin to the points of intersection of the line sqrt3x+y=2 and the curve y^(2)-x^(2)=4 is

Find the coordinates of the middle point of the portion of the straight line 2x+y=4 intercepted between the x and the y - axes.

Show that the circle x^(2) + y^(2) + 6(x-y) + 9 = 0 touches the coordinates axes. Also find the equation of the circle which passes through the common points of intersection of the above circle and the straight line x-y+4 = 0 and which also passes through the origin.