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GradePoint of Intersection of the Lines

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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) \\

$

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) \\

$

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) ${x^2} = {a^2} + {y^2}$

A) ${x^2} + {y^2} = 2{a^2}$

B) ${x^2} + {y^2} - ax = 0$

C) ${y^2} = 4ax$

D) ${x^2} = {a^2} + {y^2}$

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

Draw the graph of equation $2y+x=7$ and $2x+y=8$ on the same coordination system. Write the pt of intersection.

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 \[\overrightarrow{r}.\left( \widehat{i}-\widehat{j}+\widehat{k} \right)=5\]?

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

A. orange

B. football

C. hands of the clock

D. none of these

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.

Find the points of intersection of the line y = x - 3 and circle (x-3^{2})^{2} + (y+2)^{2} = 20.

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.$\dfrac{{ - 5}}{3}$

A.$\dfrac{{ - 2}}{5}$

B.$\dfrac{{ - 3}}{5}$

C.$\dfrac{3}{2}$

D.$\dfrac{{ - 5}}{3}$

A line through origin meets the line \[2x = 3y + 13\] at the right angle at point\[Q\]. Find the absolute difference of coordinates of\[Q\].

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. \[\left( {1,2,0} \right)\]

A. \[\left( {0,0, - 4} \right)\]

B. \[\left( {1,0,0} \right)\]

C. \[\left( {0,2,0} \right)\]

D. \[\left( {1,2,0} \right)\]

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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