If the equation of the pair of straight lines | vedclass

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

Question

(A) The given pair of lines is $3x^2 - 4xy + 5y^2 = 0$. The lines perpendicular to these and passing through $(a, b)$ have the equation $5(x-a)^2 + 4(

Vedclass · Accepted Answer

$\frac{38}{5}$

Vedclass · Answer

(A) The given pair of lines is $3x^2 - 4xy + 5y^2 = 0$. The lines perpendicular to these and passing through $(a, b)$ have the equation $5(x-a)^2 + 4(x-a)(y-b) + 3(y-b)^2 = 0$.Expanding this: $5(x^2 - 2ax + a^2) + 4(xy - bx - ay + ab) + 3(y^2 - 2by + b^2) = 0$.$5x^2 + 4xy + 3y^2 - (10a + 4b)x - (4a + 6b)y + (5a^2 + 4ab + 3b^2) = 0$.Comparing with $lx^2 + 2hxy + my^2 - 32x - 26y + c = 0$,we get $l=5, 2h=4 \implies h=2, m=3$.$10a + 4b = 32 \implies 5a + 2b = 16$.$4a + 6b = 26 \implies 2a + 3b = 13$.Solving these,$a=2, b=3$.Then $c = 5(2)^2 + 4(2)(3) + 3(3)^2 = 20 + 24 + 27 = 71$.Finally,$\frac{a+b+c}{l+h+m} = \frac{2+3+71}{5+2+3} = \frac{76}{10} = \frac{38}{5}$.

If the equation of the pair of straight lines intersecting at $(a, b)$ and perpendicular to the pair of lines $3x^2 - 4xy + 5y^2 = 0$ is $lx^2 + 2hxy + my^2 - 32x - 26y + c = 0$,then $\frac{a+b+c}{l+h+m} =$

Similar Questions

If the pair of lines represented by $3x^2 - 5xy + Py^2 = 0$ and $6x^2 - xy - 5y^2 = 0$ have one line in common,then the sum of all possible values of $P$ is

The combined equation of the diagonals of the square formed by the two pairs of straight lines given by $xy+4x-3y-12=0$ and $xy-3x+4y-12=0$ is

If the pair of straight lines given by $Ax^2+2Hxy+By^2=0$ $(H^2>AB)$ forms an equilateral triangle with the line $ax+by+c=0$,then $(A+3B)(3A+B)$ is equal to:

If the area of the triangle formed by the lines $y=x+c$ and $2x^2+5xy+3y^2=0$ is $\frac{1}{20}$ sq. units,then $c=$

The coordinates of the orthocentre of the triangle formed by the lines $2x^2 - 2y^2 + 3xy + 3x + y + 1 = 0$ and $3x + 2y + 1 = 0$ are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module