The joint equation of the pair of lines passi | vedclass

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

Question

(A) Let $\phi(x, y) = 2x^{2}-xy-15y^{2}-7x+32y-9=0$ ...$(1)$To find the point of intersection,we take partial derivatives:$\frac{\partial \phi}{\parti

Vedclass · Accepted Answer

$xy-x-2y+2=0$

Vedclass · Answer

(A) Let $\phi(x, y) = 2x^{2}-xy-15y^{2}-7x+32y-9=0$ ...$(1)$To find the point of intersection,we take partial derivatives:$\frac{\partial \phi}{\partial x} = 4x-y-7=0$ ...$(2)$$\frac{\partial \phi}{\partial y} = -x-30y+32=0$ ...$(3)$Solving equations $(2)$ and $(3)$:From $(2)$,$y = 4x-7$.Substitute into $(3)$: $-x - 30(4x-7) + 32 = 0$ $\Rightarrow -x - 120x + 210 + 32 = 0$ $\Rightarrow -121x + 242 = 0$ $\Rightarrow x = 2$.Then $y = 4(2)-7 = 1$.So,the point of intersection is $(2, 1)$.The lines passing through $(2, 1)$ parallel to the coordinate axes are $x=2$ and $y=1$.The joint equation is $(x-2)(y-1) = 0$.Expanding this,we get $xy - x - 2y + 2 = 0$.

The joint equation of the pair of lines passing through the point of intersection of the lines represented by $2x^{2}-xy-15y^{2}-7x+32y-9=0$ and parallel to the coordinate axes is:

Similar Questions

If the lines represented by $x^2-2hxy-y^2=0$ are rotated about $(0,0)$ through an angle $\alpha$,one in the clockwise direction and the other in the counter-clockwise direction,then the combined equation of the bisectors of the angle between the lines thus obtained is

If the equation $2x^2 + kxy - 6y^2 + 3x + y + 1 = 0$ $(k > 0)$ represents a pair of straight lines,then their point of intersection is

The equation of the bisectors of the angles between the lines represented by ${x^2} + 2xy \cot \theta + {y^2} = 0$ is

If the lines represented by $x^2 - 2pxy - y^2 = 0$ are rotated about the origin by an angle $\theta$ in clockwise and counter-clockwise directions respectively,then the equation of the bisector of the angle between the lines in the new position is:

The joint equation of the bisectors of the angles between the lines represented by $2x^2 + 11xy + 3y^2 = 0$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module