The angle between the lines represented by x^ | vedclass

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

Question

(A) The given equation is $x^2 - y^2 - 2y - 1 = 0$. This can be rewritten as $x^2 - (y^2 + 2y + 1) = 0$. This simplifies to $x^2 - (y + 1)^2 = 0$. Usi

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(A) The given equation is $x^2 - y^2 - 2y - 1 = 0$. This can be rewritten as $x^2 - (y^2 + 2y + 1) = 0$. This simplifies to $x^2 - (y + 1)^2 = 0$. Using the difference of squares formula $a^2 - b^2 = (a - b)(a + b)$,we get: $(x - (y + 1))(x + (y + 1)) = 0$. $(x - y - 1)(x + y + 1) = 0$. Thus,the two lines are $L_1: x - y - 1 = 0$ and $L_2: x + y + 1 = 0$. The slopes of these lines are $m_1 = 1$ and $m_2 = -1$. Since $m_1 	imes m_2 = 1 	imes (-1) = -1$,the lines are perpendicular to each other. Therefore,the angle between them is $90^o$.

The angle between the lines represented by $x^2 - y^2 - 2y - 1 = 0$ is .....$^o$

Similar Questions

Find the angle between the lines represented by $2x^2 - 7xy + 3y^2 = 0$ in degrees. (in $^o$)

If the angle between the pair of lines given by the equation $ax^2+4xy+2y^2=0$ is $45^{\circ}$,then the possible values of $a$ are:

The acute angle between the lines represented by $({x^2} + {y^2})\sqrt{3} = 4xy$ is

The angle between the lines represented by $ax^2 + 2hxy + by^2 = 0$ is:

The equation $4x^2 + 12xy + 9y^2 + 2gx + 2fy + c = 0$ represents two real parallel straight lines,if

Vedclass Test Series

Exam Paper Generator

Online Exam Module