Tag: mathematics and statistics

The area of the triangle formed by the asymptotes and any tangent to the hyperbola ${x}^{2}-{y}^{2}={a}^{2}$ is 

If foci of hyperbola lie on $y=x$ and one of the asymptote is $y=2x$, then equation of the hyperbola, given that is passes through $(3, 4)$ is :

The combined equation of the asymptotes of the hyperbola $2{x}^{2}+5xy+2{y}^{2}+4x+5y=0$ is

The ordinate of any point P on the hyperbola, given by  $25x^2-16y^2=400$, is produced to cut its asymptotes in the points Q and R, then $QP.PR=5.$

If the x-y+4=0 and x+y+2=0 are asymptotes of a hyperbola , the its center is 

A chord $AB$ which bisected at $(1,1)$ is drawn to the hyperbola $7x^{2}+8xy-y^{2}-4=0$ with centre $C$. which intersects its asymptotes in $E$ and $F$. If equation of circumcricel of $\triangle CEF$ is $x^{2}+y^{2}-ax-by+c=0$, then value of $\dfrac{23(a-b+c)}{12}$ is equal to 

The product of the lengths of perpendiculars drawn from any point on the hyperbola $x^{2}-2y^{2}-2=0$ to its asymptotes is 

The angle between the asymptotes of the hyperbola $\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}=1$, the length of whose latus rectum is $\dfrac{4}{3}$ and hyperbola passes through the point $(4,2)$ is :

The angle between the asymptotes of a hyperbola is $30^{o}$. The eccentricity of the hyperbola may be

If the equation $3x^{2}+xy-y^{2}-3x+6y+2=0$ represents hyperbola then equation of the asymptotes is given by