Straight LineHardBloom L3
Question
The equations of the lines through ( $- 1, - 1$ ) and making angle $45^{\circ}$ with the line $x + y = 0$ are given by :
Options
A.$x^{2} - xy + x - y = 0$
B.$xy - y^{2} + x - y = 0$
C.$xy + x + y = 0$
D.$xy + x + y + 1 = 0$
Solution
Sol. [Key Concept: Lines through $( - 1, - 1)$ at $45{^\circ}$ to $x + y = 0$ have slopes $0$ and $\infty$ ⇒ pair $xy + x + y + 1 = 0$.]
Equation of pair $PA$ and $PB$ is
$$\begin{matrix} (x + 1)(y + 1) & \ = 0 \\ \Rightarrow \ xy + x + y + 1 & \ = 0 \end{matrix}$$
Create a free account to view solution
View Solution FreeMore Straight Line Questions
Area of the triangle formed by the line $x + y = 3$ and angle bisector of the pair of straight lines $x^{2} - y^{2} + 2y...The least area of a quadrilateral with integral coordinates is:...The points $A(0,0),B(cos\alpha,sin\alpha)$ and $C(cos\beta,sin\beta)$ are the vertices of a right-angled triangle if:...The equation of line passing through (2, 3) and perpendicular to the line adjoining the points (−5, 6) and (−...If ω = and |ω| = 1, then z lies on...