The parametric equation of a line is given by x = - 2 + rsqrt 10 and y = 1 + 3rsqrt 10 . Then, for the line :

The cartesian equation is x + 2 = y - 13,i.e.,3x - y + 7 = 0.

the parametric equation of a line is given by x 2 10 and y

The parametric equation of a line is given by $$x = - 2 + \frac{r}{{\sqrt {10} }}$$ and $$y = 1 + 3\frac{r}{{\sqrt {10} }}.$$ Then, for the line :

A. intercept on the $$x$$-axis $$ = \frac{7}{3}$$

B. intercept on the $$y$$-axis $$ = - 7$$

C. slope of the line $$ = {\tan ^{ - 1}}\frac{1}{3}$$

D. slope of the line $$ = {\tan ^{ - 1}}3$$

Answer : slope of the line $$ = {\tan ^{ - 1}}3$$

Solution :
The cartesian equation is $$x + 2 = \frac{{y - 1}}{3},\,{\text{i}}{\text{.e}}{\text{.}},\,3x - y + 7 = 0.$$

Releted MCQ Question on
Geometry >> Straight Lines

Releted Question 1

The points $$\left( { - a, - b} \right),\left( {0,\,0} \right),\left( {a,\,b} \right)$$ and $$\left( {{a^2},\,ab} \right)$$ are :

A. Collinear

B. Vertices of a parallelogram

C. Vertices of a rectangle

D. None of these

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Releted Question 2

The point (4, 1) undergoes the following three transformations successively.
(i) Reflection about the line $$y =x.$$
(ii) Translation through a distance 2 units along the positive direction of $$x$$-axis.
(iii) Rotation through an angle $$\frac{p}{4}$$ about the origin in the counter clockwise direction.
Then the final position of the point is given by the coordinates.

A. $$\left( {\frac{1}{{\sqrt 2 }},\,\frac{7}{{\sqrt 2 }}} \right)$$

B. $$\left( { - \sqrt 2 ,\,7\sqrt 2 } \right)$$

C. $$\left( { - \frac{1}{{\sqrt 2 }},\,\frac{7}{{\sqrt 2 }}} \right)$$

D. $$\left( {\sqrt 2 ,\,7\sqrt 2 } \right)$$

View Answer

Releted Question 3

The straight lines $$x + y= 0, \,3x + y-4=0,\,x+ 3y-4=0$$ form a triangle which is-

A. isosceles

B. equilateral

C. right angled

D. none of these

View Answer

Releted Question 4

If $$P = \left( {1,\,0} \right),\,Q = \left( { - 1,\,0} \right)$$ and $$R = \left( {2,\,0} \right)$$ are three given points, then locus of the point $$S$$ satisfying the relation $$S{Q^2} + S{R^2} = 2S{P^2},$$ is-

A. a straight line parallel to $$x$$-axis

B. a circle passing through the origin

C. a circle with the centre at the origin

D. a straight line parallel to $$y$$-axis

View Answer

The parametric equation of a line is given by $$x = - 2 + \frac{r}{{\sqrt {10} }}$$ and $$y = 1 + 3\frac{r}{{\sqrt {10} }}.$$ Then, for the line :

Releted MCQ Question on
Geometry >> Straight Lines

The points $$\left( { - a, - b} \right),\left( {0,\,0} \right),\left( {a,\,b} \right)$$ and $$\left( {{a^2},\,ab} \right)$$ are :

The straight lines $$x + y= 0, \,3x + y-4=0,\,x+ 3y-4=0$$ form a triangle which is-

If $$P = \left( {1,\,0} \right),\,Q = \left( { - 1,\,0} \right)$$ and $$R = \left( {2,\,0} \right)$$ are three given points, then locus of the point $$S$$ satisfying the relation $$S{Q^2} + S{R^2} = 2S{P^2},$$ is-

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Straight Lines

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The parametric equation of a line is given by $$x = - 2 + \frac{r}{{\sqrt {10} }}$$ and $$y = 1 + 3\frac{r}{{\sqrt {10} }}.$$ Then, for the line :

Releted MCQ Question on Geometry >> Straight Lines

The points $$\left( { - a, - b} \right),\left( {0,\,0} \right),\left( {a,\,b} \right)$$ and $$\left( {{a^2},\,ab} \right)$$ are :

The straight lines $$x + y= 0, \,3x + y-4=0,\,x+ 3y-4=0$$ form a triangle which is-

If $$P = \left( {1,\,0} \right),\,Q = \left( { - 1,\,0} \right)$$ and $$R = \left( {2,\,0} \right)$$ are three given points, then locus of the point $$S$$ satisfying the relation $$S{Q^2} + S{R^2} = 2S{P^2},$$ is-

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Releted MCQ Question on
Geometry >> Straight Lines

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Straight Lines