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CBSE
Mathematics
Point of intersection of the lines
Determine graphically the vertices of the triangle, the equations of whose sides are given below:
y=x, y=0 and 3x+3y=10
 $ {\text{A}}{\text{. }}\left( {0,0} \right),\left( {\dfrac{{10}}{3},0} \right),\left( {\dfrac{5}{3},\dfrac{5}{3}} \right) \\
  {\text{B}}{\text{. }}\left( {0,0} \right),\left( {\dfrac{{17}}{3},0} \right),\left( {\dfrac{5}{3},\dfrac{5}{3}} \right) \\
  {\text{C}}{\text{. }}\left( {0,0} \right),\left( {\dfrac{{14}}{3},0} \right),\left( {\dfrac{5}{3},\dfrac{5}{3}} \right) \\
  {\text{D}}{\text{. }}\left( {0,0} \right),\left( {\dfrac{{10}}{3},0} \right),\left( {\dfrac{5}{3},\dfrac{8}{3}} \right) \\
$
CBSE
Mathematics
Point of intersection of the lines
Locus of the point of the intersection of the lines \[xcos\theta = y\] and \[cot\theta = a\] is
A) ${x^2} + {y^2} = 2{a^2}$
B) ${x^2} + {y^2} - ax = 0$
C) ${y^2} = 4ax$
D) ${x^2} = {a^2} + {y^2}$

CBSE
Mathematics
Point of intersection of the lines
How do you find the intersection between \[y = x - 8\] and \[{x^2} + {y^2} = 34\]?

CBSE
Mathematics
Point of intersection of the lines
Draw the graph of equation $2y+x=7$ and $2x+y=8$ on the same coordination system. Write the pt of intersection.
CBSE
Mathematics
Point of intersection of the lines
Find the distance of the point \[P\left( -1,-5,-10 \right)\] from the point of intersection of the line \[\overrightarrow{r}=\left( 2\widehat{i}-\widehat{j}+2\widehat{k} \right)+\lambda \left( 3\widehat{i}+3\widehat{j}+2\widehat{k} \right)\] and the plane \[\overrightarrow{r}.\left( \widehat{i}-\widehat{j}+\widehat{k} \right)=5\]?
CBSE
Mathematics
Point of intersection of the lines
Which of the following is a real-life example of intersecting lines?
A. orange
B. football
C. hands of the clock
D. none of these

CBSE
Mathematics
Point of intersection of the lines
If lines $\dfrac{x-1}{2}=\dfrac{y+1}{3}=\dfrac{z-1}{4}$ and $\dfrac{x-3}{1}=\dfrac{y-k}{2}=\dfrac{z}{1}$ intersect, then find the value of k and hence find the equation of the plane containing these lines.

CBSE
Mathematics
Point of intersection of the lines
Find the points of intersection of the line y = x - 3 and circle (x-32)2 + (y+2)2 = 20.
CBSE
Mathematics
Point of intersection of the lines
If the lines $x + ky + 3 = 0$ and $2x - 5y + 7 = 0$ intersect the coordinate axes in the concyclic points, then k=?
A.$\dfrac{{ - 2}}{5}$
B.$\dfrac{{ - 3}}{5}$
C.$\dfrac{3}{2}$
D.$\dfrac{{ - 5}}{3}$

CBSE
Mathematics
Point of intersection of the lines
A line through origin meets the line \[2x = 3y + 13\] at the right angle at point\[Q\]. Find the absolute difference of coordinates of\[Q\].
CBSE
Mathematics
Point of intersection of the lines
The point of intersection of the lines \[\dfrac{{x - 6}}{{ - 6}} = \dfrac{{y + 4}}{4} = \dfrac{{z - 4}}{{ - 8}}\] and \[\dfrac{{x + 1}}{2} = \dfrac{{y + 2}}{4} = \dfrac{{z + 3}}{{ - 2}}\] is
A. \[\left( {0,0, - 4} \right)\]
B. \[\left( {1,0,0} \right)\]
C. \[\left( {0,2,0} \right)\]
D. \[\left( {1,2,0} \right)\]

CBSE
Mathematics
Point of intersection of the lines
Draw the graph of the equation $x+3y=15$. Find the co-ordinates of the point where the graph intersects the $x$- axis.
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