## Question

The equation of the line passing through the centre of a rectangular hyperabola is *x* – *y* – 1 = 0. If one of its asymptotes is 3*x* – 4*y* – 6 = 0, the equation of the other asymptotes is

### Solution

4*x* + 3*y* + 17 = 0

The point of intersection of the line *x* – *y* – 1 = 0, which passes through the centre of the hyperbola, and the asymptotes 3*x* – 4*y* – 6 = 0 is the centre of the hyperbola. So, its coordinates are (–2, –3). Since asymptotes of a rectangular hyperbola are always at right angle. So, required asymptote is perpendicular to the given asymptote and passes through the centre (–2, –3) of the hyperbola and hence is equation is

#### SIMILAR QUESTIONS

If *e*_{1} is the eccentricity of the ellipse and e_{2} is the eccentricity of the hyperbola passing through the foci of the ellipse and *e*_{1}*e*_{2} = 1, then the equation of the parabola, is

The eccentricity of the conjugate hyperbola of the hyperbola *x*^{2} – 3*y*^{2} = 1 is

The slopes of the common tangents of the hyperbolas and

A hyperbola, having the transverse axis of the length , is confocal with the ellipse 3*x*^{2} + 4*y*^{2} = 12. Then, its equation is

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If a hyperbola passing through the origin has 3*x* – 4*y* – 1 = 0 and 4*x* – 3*y* – 6 = 0 as its asymptotes, then the equations of its transverse and conjugate axes are

If *H*(*x*, *y*) = 0 represents the equation of a hyperbola and *A*(*x*, *y*) = 0, *C*(*x*,*y*) = 0 the joint equation of its asymptotes and the conjugate hyperbola respectively, then for any point (α, β) in the plane, are in

The equation of a tangent to the hyperbola which make an angle π/4 with the transverse axis, is

For the hyperbola which of the following remains constant with change in ‘α’

If radii of director circles of are 2*r* and *r*respectively and *e _{e}* and

*e*be the eccentricities of the ellipse and hyperbola respectively, then

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