If a hyperbola passing through the origin has `3x-4y-1=0` and `4x-3y-6=0` as its asymptotes, then find the equation of its transvers and conjugate axes.

If a circle passes through the points where the lines 3kx- 2y-1 = 0 and 4x-3y + 2 = 0 meet the coordinate axes then k=

A hyperbola passes through (2,3) and has asymptotes 3x-4y+5=0 and 12 x+5y-40=0 . Then, the equation of its transverse axis is 77 x-21 y-265=0 21 x-77 y+265=0 21 x-77 y-265=0 21 x+77 y-265=0

Find the equation of the hyperbola which has 3x-4y+7=0 and 4x+3y+1=0 as its asymptotes and which passes through the origin.

An ellipse passes through the point (4,-1) and touches the line x+4y-10=0 . Find its equation if its axes coincide with the coordinate axes.

An ellipse passes through the point (4,-1) and touches the line x+4y-10=0 . Find its equation if its axes coincide with the coordinate axes.

Statement 1 : The asymptotes of hyperbolas 3x+4y=2 and 4x-3y=5 are the bisectors of the transvers and conjugate axes of the hyperbolas. Statement 2 : The transverse and conjugate axes of the hyperbolas are the bisectors of the asymptotes.

A circle passes through the origin and has its center on y=x If it cuts x^2+y^2-4x-6y+10=- orthogonally, then find the equation of the circle.

If a line passing through the origin touches the circle (x-4)^2+(y+5)^2=25 , then find its slope.

Find the asymptotes of the curve x y-3y-2x=0 .

The equatin of a line passing through the origin and perpendicular to the line 7x-3y+4=0 is