The equation of the pair of lines joining the | vedclass

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

Question

(D) Let the two circles be $S_1: x^2+y^2-4x+8y+5=0$ and $S_2: x^2+y^2+2x+4y-3=0$. The common chord is given by $S_1-S_2=0$. $(x^2+y^2-4x+8y+5) - (x^2+

Vedclass · Accepted Answer

$13x^2+68xy-28y^2=0$

Vedclass · Answer

(D) Let the two circles be $S_1: x^2+y^2-4x+8y+5=0$ and $S_2: x^2+y^2+2x+4y-3=0$. The common chord is given by $S_1-S_2=0$. $(x^2+y^2-4x+8y+5) - (x^2+y^2+2x+4y-3) = 0$ $-6x+4y+8=0 \Rightarrow 3x-2y-4=0$. Thus,the equation of the line is $3x-2y=4$,or $\frac{3x-2y}{4}=1$. To find the pair of lines joining the origin to the intersection points,we homogenize the equation of $S_2$ using the line equation: $x^2+y^2+(2x+4y)(1) - 3(1)^2 = 0$ $x^2+y^2+(2x+4y)(\frac{3x-2y}{4}) - 3(\frac{3x-2y}{4})^2 = 0$ Multiplying by $16$ to clear the denominator: $16(x^2+y^2) + 4(2x+4y)(3x-2y) - 3(9x^2+4y^2-12xy) = 0$ $16x^2+16y^2 + 4(6x^2-4xy+12xy-8y^2) - 27x^2-12y^2+36xy = 0$ $16x^2+16y^2 + 24x^2+32xy-32y^2 - 27x^2-12y^2+36xy = 0$ $(16+24-27)x^2 + (32+36)xy + (16-32-12)y^2 = 0$ $13x^2+68xy-28y^2=0$.

The equation of the pair of lines joining the origin to the points of intersection of two circles $x^2+y^2-4x+8y+5=0$ and $x^2+y^2+2x+4y-3=0$ is

Similar Questions

The equation of the pair of straight lines joining the origin to the points of intersection of the curve $x^2 + y^2 = 4$ and the line $y - x = 2$ is

If the lines joining the origin to the points of intersection of $y=mx+1$ and $x^2+y^2=1$ are perpendicular,then .........

If the distance between the parallel lines given by the equation $x^2+4xy+4y^2+3x+6y-4=0$ is $\lambda$,then $\lambda^2=$

$A$ pair of perpendicular lines passes through the origin and also through the points of intersection of the curve $x^2+y^2=4$ with $x+y=a$,where $a>0$. Then $a$ is equal to

The distance between the lines represented by the equation $x^2 + 2\sqrt{3}xy + 3y^2 - 3x - 3\sqrt{3}y - 4 = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module