Prove that the equations to the straight lines through the origin each of which makes an angle `alpha` with the straight line `y=x` is `x^(2)-2xysec2alpha+y^(2)=0`.

If x^2+2h x y+y^2=0 represents the equation of the straight lines through the origin which make an angle alpha with the straight line y+x=0 (a) s e c2alpha=h (b) cosalpha=sqrt(((1+h))/((2h))) (c) 2sinalpha =sqrt(((1+h))/h) (d) cotalpha =sqrt(((1+h))/((h-1)))

The equations of the lines through the point (3, 2) which makes an angle of 45^(@) with the line x - 2y = 3 are

Find the equation of the straight line which passes through the origin and makes angle 60^0 with the line x+sqrt(3)y+sqrt(3)=0 .

The slope of the straight line 2y=x+8 is ___.

Find the equation of the straight line through the intersection of 5x-6y=1 and 3x+2y+5=0 and perpendicular to the straight line 3x-5y+11=0

Find the equation of the straight lines touching both x^2+y^2=2a^2 and y^2=8a xdot

Find the equation of the straight line that passes through the point (3,4) and is perpendicular to the line 3x+2y+5=0

Find the equation of the straight lines, making the y-intercept of 7 and angle between the line and the y-axis is 30^(@) .