Tag: hyperbola

If a line intersect a hyperbola at $(-2,-6)$ and $(4,2)$ and one of the asymtote at $(1,-2)$, then the centre of the hyperbola is

Let product of distances of any point hyperbola (x+y-1) (x-y+3)= 60 to its asymptotes is 'K' then K is divisible by

If the cordinate of any point p on the hyperbola $9{x^2} - 16{y^2} = 144$ is produced to cut the asymptotes in the points Q and R. Then the product PQ.PR equals to:

The points of intersection of asymptotes with directrices lies on

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