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5 answers
The equations of the perpendicular bisector of the sides $A B$ and $A C$ of a $Delta A B C$ are $x-y+5=0$ and $x+$ $2 y=0$, respectively. If the point $A$ is $(1,-2)$ then the equation of the line $B C$ is(A) $14 x+23 y=40$(B) $14 x-23 y=40$(C) $23 x+14 y=40$(D) $23 x-14 y=40$
The equations of the perpendicular bisector of the sides $A B$ and $A C$ of a $Delta A B C$ are $x-y+5=0$ and $x+$ $2 y=0$, respectively. If the point $A$ is $(1,-2)$ then the equation of the line $B C$ is (A) $14 x+23 y=40$ (B) $14 x-23 y=40$ (C) $23 x+14 y=40$ (D) $23 x-14 y=40$...
4 answers
1. The equation of a family of lines is given by $(2+3 t)$ $x+(1-2 t) y+4=0$, where $t$ is the parameter. The equation of a straight line, belonging to this family, at the maximum distance from the point $(2,3)$ is(A) $21 x+14 y=0$(B) $21 x-14 y=0$(C) $14 x-21 y=0$(D) none of these
1. The equation of a family of lines is given by $(2+3 t)$ $x+(1-2 t) y+4=0$, where $t$ is the parameter. The equation of a straight line, belonging to this family, at the maximum distance from the point $(2,3)$ is (A) $21 x+14 y=0$ (B) $21 x-14 y=0$ (C) $14 x-21 y=0$ (D) none of these...
4 answers
$A B C D$ is a square whose vertices $A, B, C$ and $D$ are $(0,0),(2,0),(2,2)$ and $(0,2)$, respectively. This square is rotated in the $X-Y$ plane with an angle of $30^{circ}$ in anti-clockwise direction about an axis passing through the vertex $A$. The equation of the diagonal $B D$ of this rotated square is(A) $sqrt{3} x+(1-sqrt{3}) y=sqrt{3}$(B) $(1+sqrt{3}) x-(1-sqrt{2})=2$(C) $(2-sqrt{3}) x+y=2(sqrt{3}-1)$(D) none of these
$A B C D$ is a square whose vertices $A, B, C$ and $D$ are $(0,0),(2,0),(2,2)$ and $(0,2)$, respectively. This square is rotated in the $X-Y$ plane with an angle of $30^{circ}$ in anti-clockwise direction about an axis passing through the vertex $A$. The equation of the diagonal $B D$ of this rotate...
5 answers
The equations of the straight lines passing through $(-2,-7)$ and cutting an intercept of length three units between the straight lines $4 x+3 y=12$ and $4 x+3 y=$ 3 are(A) $x+2=0, y+7=frac{7}{24}(x+2)$(B) $x-2=0, y+7=-frac{7}{24}(x+2)$(C) $x+2=0, y+7=-frac{7}{24}(x+2)$(D) $x+2=0, y+7=-frac{7}{12}(x+2)$
The equations of the straight lines passing through $(-2,-7)$ and cutting an intercept of length three units between the straight lines $4 x+3 y=12$ and $4 x+3 y=$ 3 are (A) $x+2=0, y+7=frac{7}{24}(x+2)$ (B) $x-2=0, y+7=-frac{7}{24}(x+2)$ (C) $x+2=0, y+7=-frac{7}{24}(x+2)$ (D) $x+2=0, y+7=-frac{7}{1...
5 answers
The coordinates of the point which is at unit distance from the lines $L_{1} equiv 3 x-4 y+1=0$ and $L_{2} equiv 8 x+6 y+$ $1=0$ and lies below $L_{1}$ and above $L_{2}$ are(A) $left(frac{6}{5}, frac{1}{10}ight)$(B) $left(frac{6}{5},-frac{1}{10}ight)$(C) $left(frac{6}{5}, frac{1}{5}ight)$(D) $left(frac{6}{5},-frac{1}{5}ight)$
The coordinates of the point which is at unit distance from the lines $L_{1} equiv 3 x-4 y+1=0$ and $L_{2} equiv 8 x+6 y+$ $1=0$ and lies below $L_{1}$ and above $L_{2}$ are (A) $left(frac{6}{5}, frac{1}{10} ight)$ (B) $left(frac{6}{5},-frac{1}{10} ight)$ (C) $left(frac{6}{5}, frac{1}{5} ight)$ (D) ...
5 answers
$O X$ and $O Y$ are two coordinate axes. On $O Y$ is taken a fixed point $P$ and on $O X$ any point $Q .$ On $P Q$ an equilateral triangle is described, its vertex $R$ being on the side of $P Q$ away from $O$, then the locus of $R$ will be(A) straight line(B) circle(C) ellipse(D) parabola
$O X$ and $O Y$ are two coordinate axes. On $O Y$ is taken a fixed point $P$ and on $O X$ any point $Q .$ On $P Q$ an equilateral triangle is described, its vertex $R$ being on the side of $P Q$ away from $O$, then the locus of $R$ will be (A) straight line (B) circle (C) ellipse (D) parabola...
5 answers
If the vertices of a variable triangle are $(3,4)$, ( $5 mathrm{cos}$ $heta, 5 sin heta$ ) and $(5 sin heta,-5 cos heta)$, then the locus of itsorthocentre is(A) $(x+y-1)^{2}+(x-y-7)^{2}=100$(B) $(x+y-7)^{2}+(x-y+1)^{2}=100$(C) $(x+y-7)^{2}+(x-y-1)^{2}=100$(D) $(x+y+7)^{2}+(x+y-1)^{2}=100$
If the vertices of a variable triangle are $(3,4)$, ( $5 mathrm{cos}$ $ heta, 5 sin heta$ ) and $(5 sin heta,-5 cos heta)$, then the locus of its orthocentre is (A) $(x+y-1)^{2}+(x-y-7)^{2}=100$ (B) $(x+y-7)^{2}+(x-y+1)^{2}=100$ (C) $(x+y-7)^{2}+(x-y-1)^{2}=100$ (D) $(x+y+7)^{2}+(x+y-1)^{2}=100$...

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