The equation of the asymptotes of the hyperbo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The equation of the asymptotes of the hyperbola $2 x^2+5 x y+2 y^2-11 x-7 y-4=0$ is of the form $2 x^2+5 x y+2 y^2-11 x-7 y+\lambda=0$. Since this

Vedclass · Accepted Answer

$2 x^2+5 x y+2 y^2-11 x-7 y+5=0$

Vedclass · Answer

(B) The equation of the asymptotes of the hyperbola $2 x^2+5 x y+2 y^2-11 x-7 y-4=0$ is of the form $2 x^2+5 x y+2 y^2-11 x-7 y+\lambda=0$. Since this represents a pair of straight lines,the determinant of the general second-degree equation must be zero: $abc + 2fgh - af^2 - bg^2 - ch^2 = 0$. Here,$a=2, b=2, c=\lambda, h=\frac{5}{2}, g=-\frac{11}{2}, f=-\frac{7}{2}$. Substituting these values: $2(2)(\lambda) + 2(-\frac{7}{2})(-\frac{11}{2})(\frac{5}{2}) - 2(-\frac{7}{2})^2 - 2(-\frac{11}{2})^2 - \lambda(\frac{5}{2})^2 = 0$. $4\lambda + \frac{385}{4} - \frac{49}{2} - \frac{121}{2} - \frac{25\lambda}{4} = 0$. Multiplying by $4$: $16\lambda + 385 - 98 - 242 - 25\lambda = 0$. $-9\lambda + 45 = 0 \Rightarrow \lambda = 5$. Thus,the equation is $2 x^2+5 x y+2 y^2-11 x-7 y+5=0$.

The equation of the asymptotes of the hyperbola $2 x^2+5 x y+2 y^2-11 x-7 y-4=0$ is

Similar Questions

The equations of the transverse and conjugate axes of the hyperbola $16x^2 - y^2 + 64x + 4y + 44 = 0$ are

If the eccentricities of two conics $S$ and $S'$ are $e$ and $e'$ respectively,such that $e^2 + e'^2 = 3$,then both $S$ and $S'$ are:

The area of the quadrilateral formed by the foci of the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$ and its conjugate hyperbola is (in square units):

If $x = 9$ is a chord of contact of the hyperbola $x^2 - y^2 = 9$,then the equation of the corresponding pair of tangents is...

Consider a branch of the hyperbola $x^2 - 2y^2 - 2\sqrt{2}x - 4\sqrt{2}y - 6 = 0$ with vertex at the point $A$. Let $B$ be one of the end points of its latus rectum. If $C$ is the focus of the hyperbola nearest to the point $A$,then the area of the triangle $ABC$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module