A divides CB in 2:1 ⇒4=(1+21×0+2×a)=32a⇒a=6⇒ coordinate of B is B (6,0)3=(1+21×b+2×0)=3b⇒b=9 and C(0,9) Slope of line passing through (6,0),(0,9) slope, m=−69=−23 Equation of line y−0=2−3(x−6) 2y=−3x+183x+2y=18
If a line intercepted between the coordinate axes is trisected at a point A(4,3), which is nearer to x-axis, then its equation is:
Held on 12 Apr 2014 · Verified 6 Jul 2026.
4x−3y=7
3x+2y=18
3x+8y=36
x+3y=13
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Let the image of parabola $x^{2}=4 y$, in the line $x-y=1$ be $(y+a)^{2}=b(x-c)$, $a, b, c \in \mathrm{~N}$. Then $a+b+c$ is equal to
The distance between the points (3, 4) and (6, 8) is:
If the chord joining the points $\mathrm{P}_{1}\left(x_{1}, y_{1}\right)$ and $\mathrm{P}_{2}\left(x_{2}, y_{2}\right)$ on the parabola $y^{2}=12 x$ subtends a right angle at the vertex of the parabola, then $x_{1} x_{2}-y_{1} y_{2}$ is equal to
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Let a point $A$ lie between the parallel lines $L_{1}$ and $L_{2}$ such that its distances from $L_{1}$ and $L_{2}$ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle $A B C$, where the points $B$ and C lie on the lines $\mathrm{L}_{1}$ and $\mathrm{L}_{2}$, respectively, is :
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