If one of the lines of the pair of straight l | vedclass

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

Question

(B) The given pair of straight lines is $ax^2 + 2hxy + by^2 = 0$. Since one of the lines bisects the angle between the coordinate axes,its slope $m$ m

Vedclass · Accepted Answer

$(a + b)^2 = 4h^2$

Vedclass · Answer

(B) The given pair of straight lines is $ax^2 + 2hxy + by^2 = 0$. Since one of the lines bisects the angle between the coordinate axes,its slope $m$ must be $	an(45^{\circ}) = 1$ or $	an(135^{\circ}) = -1$. If $m = 1$,the line is $y = x$. Substituting $y = x$ into the equation $ax^2 + 2hxy + by^2 = 0$,we get: $ax^2 + 2hx(x) + b(x)^2 = 0$ $ax^2 + 2hx^2 + bx^2 = 0$ $(a + 2h + b)x^2 = 0$ This implies $a + b + 2h = 0$,or $a + b = -2h$. Squaring both sides,we get $(a + b)^2 = (-2h)^2 = 4h^2$. If $m = -1$,the line is $y = -x$. Substituting $y = -x$ into the equation,we get: $ax^2 + 2hx(-x) + b(-x)^2 = 0$ $ax^2 - 2hx^2 + bx^2 = 0$ $(a - 2h + b)x^2 = 0$ This implies $a + b = 2h$. Squaring both sides,we get $(a + b)^2 = (2h)^2 = 4h^2$. In both cases,the result is $(a + b)^2 = 4h^2$.

If one of the lines of the pair of straight lines $ax^2 + 2hxy + by^2 = 0$ bisects the angle between the coordinate axes,then:

Similar Questions

The equation of the pair of straight lines perpendicular to the pair $2 x^2+3 x y+2 y^2+10 x+5 y=0$ and passing through the origin is $..........$

For $a, b, h > 0$,if the slope of one of the lines represented by $a^2 x^2 + 2hxy + b^2 y^2 = 0$ is twice that of the other,then the value of $\frac{h}{ab}$ is

The equation of the pair of lines passing through the origin whose sum and product of slopes are respectively the arithmetic mean and geometric mean of $4$ and $9$ is

If one of the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ bisects the angle between the coordinate axes in the first quadrant,then which of the following is true?

If $x^2-y^2+2hxy+2gx+2fy+c=0$ is the locus of a point which moves such that it is always equidistant from the lines $x+2y+7=0$ and $2x-y+8=0$,then the value of $g+c+h-f$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module