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.
Text Solution
Verified by Experts
The axes of a hyperbola are the bisectors of the pair of asymptotes. The tranverse axis is the bisector which contains the origin and is given `(3x-4y-1)/(5)=+(4x-3y-6)/(5)` `"or "x+y-5=0` The conjugate axis is `(3x-4y-1)/(5)=-(4x-3y-6)/(5)` `"or "x-y-1=0`
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:
A circle passes through the points (-3, 4), (1, 0) and its centre lies on the x-axis. Find the equation of the circle.
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.
A circle passes through the origin and has its center on y=x If it cuts x^2+y^2-4x-6y+10=0 orthogonally, then find the equation of the circle.
Find the equation of the straight line which passes through the point of intercestion of the straight lines 3x-4y+1=0 and 5x+y=0 and makes equal intercepts upon the coordinate axes .
Find the asymptotes of the curve x y-3y-2x=0 .
Find the equation of the line passing through the point of intersection of the lines 4x + 7y - 3 = 0 " and " 2x - 3y + 1 = 0 that has equal intercepts on the axes.
Find the equation of the staight line passing through the point of intersection of the straight lines 2x+3y+4=0 and 3x+y-1=0 and inclined to the positive direction of the x - axis at an angle 135^(@) .
Find the equation of the circle which passes through the origin and cuts off intercepts 3 unit and 4 unit from x and y-axes respectively. Find the equation of that diameter of the circle which passes through the origin.
