1
JEE Main 2024 (Online) 30th January Evening Shift
+4
-1

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

A
8
B
14
C
29
D
6
2
JEE Main 2024 (Online) 30th January Morning Shift
+4
-1

A line passing through the point $$\mathrm{A}(9,0)$$ makes an angle of $$30^{\circ}$$ with the positive direction of $$x$$-axis. If this line is rotated about A through an angle of $$15^{\circ}$$ in the clockwise direction, then its equation in the new position is :

A
$$\frac{y}{\sqrt{3}+2}+x=9$$
B
$$\frac{x}{\sqrt{3}+2}+y=9$$
C
$$\frac{x}{\sqrt{3}-2}+y=9$$
D
$$\frac{y}{\sqrt{3}-2}+x=9$$
3
JEE Main 2024 (Online) 29th January Evening Shift
+4
-1

Let $$\mathrm{A}$$ be the point of intersection of the lines $$3 x+2 y=14,5 x-y=6$$ and $$\mathrm{B}$$ be the point of intersection of the lines $$4 x+3 y=8,6 x+y=5$$. The distance of the point $$P(5,-2)$$ from the line $$\mathrm{AB}$$ is

A
$$\frac{13}{2}$$
B
8
C
$$\frac{5}{2}$$
D
6
4
JEE Main 2024 (Online) 29th January Evening Shift
+4
-1

The distance of the point $$(2,3)$$ from the line $$2 x-3 y+28=0$$, measured parallel to the line $$\sqrt{3} x-y+1=0$$, is equal to

A
$$3+4 \sqrt{2}$$
B
$$6 \sqrt{3}$$
C
$$4+6 \sqrt{3}$$
D
$$4 \sqrt{2}$$
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