1
COMEDK 2024 Morning Shift
+1
-0

The perpendicular distance of a line from the origin is 5 units and its slope is $$-1$$. The equation of the line is

A
$$x+y \pm 5 \sqrt{2}=0$$
B
$$x-y \pm 2 \sqrt{5}=0$$
C
$$x+y \pm 2 \sqrt{5}=0$$
D
$$x-y \pm 5 \sqrt{2}=0$$
2
COMEDK 2023 Morning Shift
+1
-0

Let the equation of pair of lines $$y=m_1 x$$ and $$y=m_2 x$$ can be written as $$\left(y-m_1 x\right)\left(y-m_2 x\right)=0$$. Then, the equation of the pair of the angle bisector of the line $$3 y^2-5 x y-2 x^2=0$$ is

A
$$x^2+5 x y-y^2=0$$
B
$$x^2-5 x y+y^2=0$$
C
$$x^2-x y+y^2=0$$
D
$$x^2+x y-y^2=0$$
3
COMEDK 2023 Morning Shift
+1
-0

The distance of the point $$(3,4)$$ from the line $$3 x+2 y+7=0$$ measured along the line parallel to $$y-2 x+7=0$$ is equal to

A
$$\frac{24 \sqrt{5}}{7}$$
B
$$3 \sqrt{5}$$
C
$$\frac{23 \sqrt{5}}{7}$$
D
$$4 \sqrt{5}$$
4
COMEDK 2023 Morning Shift
+1
-0

The slope of lines which makes an angle $$60^{\circ}$$ with the line $$y-3 x+18=0$$

A
$$\frac{3 \sqrt{3}-3}{1+3 \sqrt{3}}, \frac{3 \sqrt{3}-3}{1+3 \sqrt{3}}$$
B
$$\frac{3-\sqrt{3}}{1+3 \sqrt{3}}, \frac{3+\sqrt{3}}{1-3 \sqrt{3}}$$
C
$$\frac{3}{1+\sqrt{3}}, \frac{3}{1-\sqrt{3}}$$
D
$$\frac{\sqrt{3}-1}{3}, \frac{\sqrt{3}+1}{3}$$
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