The lines represented by the equation x^2-y^2 | vedclass

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

Question

(D) The given equation is $x^2-y^2-x+3y-2=0$. We can rewrite the equation by grouping terms: $x^2 - (y^2 - 3y + 2) = 0$. Factor the quadratic expressi

Vedclass · Accepted Answer

$x-y+1=0, x+y-2=0$

Vedclass · Answer

(D) The given equation is $x^2-y^2-x+3y-2=0$. We can rewrite the equation by grouping terms: $x^2 - (y^2 - 3y + 2) = 0$. Factor the quadratic expression in $y$: $y^2 - 3y + 2 = (y-1)(y-2)$. So,$x^2 - (y-1)(y-2) = 0$. This does not immediately factor as a difference of squares. Let us expand the options to check. Consider option $D$: $(x-y+1)(x+y-2) = x(x+y-2) - y(x+y-2) + 1(x+y-2) = x^2 + xy - 2x - xy - y^2 + 2y + x + y - 2 = x^2 - y^2 - x + 3y - 2$. This matches the given equation. Therefore,the lines are $x-y+1=0$ and $x+y-2=0$.

The lines represented by the equation $x^2-y^2-x+3y-2=0$ are :

Similar Questions

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

The combined equation of the pair of lines passing through the origin and perpendicular to the pair of lines $2x^2 - xy - y^2 = 0$ is:

If $4ab = 3h^2$,then the ratio of the slopes of the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ will be

The lines ${a^2}{x^2} + bc{y^2} = a(b + c)xy$ will be coincident,if

For what value of $p$ does the equation $y^2 + xy + px^2 - x - 2y = 0$ represent two straight lines?

Vedclass Test Series

Exam Paper Generator

Online Exam Module