If one of the lines represented by ax^2+2hxy+ | vedclass

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

Question

(B) The equation $ax^2+2hxy+by^2=0$ represents a pair of lines passing through the origin $(0,0)$.Since one line passes through $(0,0)$ and $(2,3)$,it

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) The equation $ax^2+2hxy+by^2=0$ represents a pair of lines passing through the origin $(0,0)$.Since one line passes through $(0,0)$ and $(2,3)$,its equation is $y - 0 = \frac{3-0}{2-0}(x - 0)$,which simplifies to $3x - 2y = 0$.Since the other line passes through $(0,0)$ and $(4,5)$,its equation is $y - 0 = \frac{5-0}{4-0}(x - 0)$,which simplifies to $5x - 4y = 0$.The joint equation of these two lines is $(3x - 2y)(5x - 4y) = 0$.Expanding this,we get $15x^2 - 12xy - 10xy + 8y^2 = 0$,which is $15x^2 - 22xy + 8y^2 = 0$.Comparing this with $ax^2 + 2hxy + by^2 = 0$,we get $a = 15$,$2h = -22$ (so $h = -11$),and $b = 8$.Therefore,$a + 2h + b = 15 - 22 + 8 = 1$.

If one of the lines represented by $ax^2+2hxy+by^2=0$ passes through $(2,3)$ and the other passes through $(4,5)$,then $a+2h+b$ equals

Similar Questions

In how many ways can a team of $10$ players be selected from $22$ players,such that $6$ particular players are always included and $4$ particular players are always excluded?

The area (in square units) of the region bounded by $x^2=8y$,$x=4$ and the $X$-axis is:

Which of the following is an example of somatic hybridization?

At high temperatures,which of the following are present?

Which of the following pairs of transition metal ions have the same calculated values of magnetic moment?

Vedclass Test Series

Exam Paper Generator

Online Exam Module