Chapter 4 | Introduction to Analytic Geometry | Entry Test Preparation

Welcome to your Chapter 4(Introduction to Analytical Geometry)

Name

Class

The measure of the angle $\theta$ from the line $p_1x+q_1x+r_1=0$ to the line $p_2x+q_2y+r_2=0$, is given by $\tan{\theta}$=______;

None of these

$\frac{p_1q_1+p_2q_2}{p_1q_2-p_2q_1}$

$\frac{p_1q_2+q_2q_1}{p_1q_2-p_2q_1}$

$\frac{p_1q_2+p_2q_1}{p_1p_2-p_1q_2}$

None

The area of the triangle formed by the lines $7x-y-10=0$, $10x+y-41=0$ and $3x+2y+3=0$ is;

34 square units

68 square units

17 square units

7.5 square units

None

The equation of the line through the point $(-2,1)$ and the point of interaction of the lines $4x+3y-1=0$ and $2x-6y+5=0$ is;

$18x+29y-21=0$

$23x-43y+27=0$

$8x+51y-35=0$

$x-13y+19=0$

None

The slope formula is given by;

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{y_2+y_1}{x_2+x_1}$

$m=\frac{x_2+x_1}{y_2+y_1}$

$m=\frac{y_2+y_1}{x_2-x_1}$

None

The inclination of any line parallel to y-axis is

$\frac{\pi}{4}$

$0$

$\frac{3\pi}{2}$

$\frac{\pi}{2}$

None

Joint equation of lines through the origin and perpendicular to the lines $x^2+xy-6y^2=0$

$-6x^2+x+y^2=0$

$6x^2+xy-y^2=0$

None of these

$-6x^2-xy-y^2=0$

None

Which point is above the line $\frac{4}{3}x+y=1?$

$(3,1)$

$(-4,-1)$

$(-3,1)$

$(-3,-1)$

None

The points $(4, -2), (-2, 4)$ and $(5, 5)$ are the vertices of a triangle. Then the coordinates of the in centre of the triangle are _______ ?

$(\frac{7}{2}, \frac{2}{7})$

$(\frac{5}{2}, \frac{5}{2})$

$(3, -3)$

$(\frac{3}{2}, \frac{3}{2})$

None

Two lines are parallel if and only if they have same;

Distance

quadrants

slope

vertices

None

Centroid of a triangle with vertices $A(2, 3), B(-1, 6)$ and $C(7, 5)$ is

$(\frac{8}{3}, \frac{14}{3})$

$(\frac{1}{3}, \frac{2}{7})$

$(\frac{2}{5}, \frac{7}{3})$

$(\frac{7}{3}, \frac{11}{3})$

None

The equation of line through $(x_2, y_2)$ perpendicular to the line $px+qy+r=0$ is;

$px+qy+px_2+qy_2=0$

$px_2+qy_2+3px-3qy=0$

$qx_2-py_2-qx+py=0$

$px_2+qy_2=0$

None

The distance between the parallel lines $4x+3y-2=0$ and $4x+3y+8=0$ is;

$2$

$12$

$\frac{59}{3}$

$\frac{13}{2}$

None

If $\overline{AB}:\overline{BC}=2:3$ then point C divides the line segment $AB$ externally in ratio

$3:5$

$2:3$

$1:3$

$3:2$

None

Slope of line parallel to $x-axis$ is;

$0$

$1$

$2$

$\infty$

None

The line segment joining by the points $(-3,-4)$ and $(1,-2)$ is divide by y-axis in the ratio

$2:3$

$3:1$

$1:3$

$3:2$

None

The matrix form of the system of linear equations; $3x+4y-7=0$ , $2x-5y+8=0$ , $x+y-3=0$

None of these

$\begin{bmatrix} 3 & 4 & -7 \\ 2 & -5 & 8 \\ 1 & 1 & -3 \end{bmatrix}$$\begin{bmatrix} x \\ y \\ z \end{bmatrix}$$=\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}$

$\begin{bmatrix} 3x+4y-7=0 \\ 2x-5y+8=0 \\ x+y-3=0 \end{bmatrix}$

$\begin{bmatrix} 3 & 4 & -7 \\ 2 & -5 & 8 \\ 1 & 1 & -3 \end{bmatrix}$$\begin{bmatrix} x \\ y \\ 1 \end{bmatrix}$$=\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}$

None

$A(0,b), B(0,0)$ and $C(a,0)$ are vertices of a triangle. Its median AD and mutually perpendicular if;

$a=\pm\sqrt{2}b$

$a=\sqrt{2}b$

$b=-\sqrt{2}a$

$a=\frac{b}{\sqrt{2}}$

None

Which pair of line are $\perp$ to each other?

$x-2y-6=0,\,2x+y-5=0$

$4x+3y-7=0,\,2x+7y+4=0$

$7x-3y=17,\,5x+2y=9$

$2x+2y=1,\,3x+3y=1$

None

Distance of the point $(-7,13)$ from the line $2x+y+13=0$ is;

$56$

$\frac{6}{\sqrt{109}}$

$67$

$\frac{12}{\sqrt{5}}$

None

The equation of line through $(-3, 5)$ and $\perp$ to line $x+2y+3=0$ is;

$2x-y+11=0$

$4y+13x=19$

$y+2x+7=0$

$3x+7y+20=0$

None

The points $(7, 9), (3, -7)$ and $(-3, 3)$ are the vertices of

An equilateral $\Delta$

A right angled isosceles $\Delta$

An isosceles $\Delta$

A right angled $\Delta$

None

The equation of the line through the points $(2,4)$ and $(7,1)$ is;

$9x+2y+17$

$5y+3x=0$

$5y+3x-26=0$

$2\sqrt{5}y+16x-13$

None

Point of intersection of pair of lines $7x+2y=6$ and $3x+y=0$;

$(6, -18)$

$(3,\,-\frac{1}{2})$

$(-6,-1)$

$(17,9)$

None

The xy-coordinates are rotated about origin at an angle $180^o$ , then the coordinates of the point $P(4,-1)$ are;

$(-4,-1)$

$(-1,4)$

$(-4,1)$

$(1,4)$

None

The inclination of the x-axis is;

$150^{o}$

$180^{o}$

$0^{o}$

$90^{o}$

None

Any equation of first degree in x and y represents a;

rectangle

Triangle

quadratic equation

line

None

Slope of a line parallel to y-axis is;

undefined

$0$

$1$

$-1$

None

The measure of the angle from the first line to the second line whose slopes are $0$ and $3$, is;

$\tan^{-1}(\frac{1}{3})$

$\tan^{-1}(3)$

$\frac{1}{2}\tan^{-1}(7)$

$2\tan^{-1}(3)$

None

Directed between the lines $4x+3y=11$ and $ 8x+6y=15$ is _________.

$\frac{7}{2}$

$4$

$\frac{15}{10}$

$\frac{7}{10}$

None

If the sum of the distances of a point from two $\perp$ lines is 1 then the locus is ___-

two intersecting straight lines

straight line

circle

square

None

The average entry test score of engineering candidates was 592 in the year 1998, while the score was 564 in 2002. assuming that the relationship between time and score is linear, then the average score in the year 2006 will be;

$450$

$650$

$536$

$350$

None

Find $'b'$ if the line through $(3,4)$ and $(-1,b)$ is parallel to the line through $(2,3)$ and $(-4,1)$.

$17$

$-\frac{11}{15}$

$20$

$\frac{20}{7}$

None

Which is the intercept form of the equation $px+qy+r=0$?

None

$x\cos{\alpha}+y\sin{\alpha}=1$

$y=mx+r$

$\frac{x}{p}+\frac{y}{q}=1$

None

The equation of the straight line through the point of intersection of $16x-10y-33=0, 12x+14y+29=0$ and the intersection of $x-y+4=0, x-7y+2=0$ is;

$13x-29y-66=0$

$13x+29y+66=0$

$13x+29y-66=0$

$13x-29y+66=0$

None

If the gradient of the line passing through $A(3,2)$ is $\frac{3}{4}$, the points on the at a distance 5 units from A are;

$(-7,5), (-1,-1)$

$(-7,-5), (1,1)$

$(7,5), (-1,-1)$

$(1,1), (5,-5)$

None

The points $(5,-2), (1,2), (-2,5)$ are;

Collinear

vertices of rectangle

all

Vertices of $\triangle$

None

Equation of hypotenuse $\overline{AB}$ of length $\sqrt{2}$ in isosceles $\triangle \, OAB$ is

$\sqrt{2}x+y=1$

$x+y=1$

$x+y=\sqrt{2}$

$x+\sqrt{2y}=1$

None

The vertices of a $\triangle \, ABC$ are $(2,2), (-4,-4)$ and $(5,-8)$ respectively, the length of the median through C is_________

$\sqrt{117}$

$\sqrt{65}$

$\sqrt{85}$

$\sqrt{113}$

None

$y=-\frac{17}{9}x+\frac{37}{9}$ is _______ form equation $9y+17x-37=0$.

point - Slope

Slope-intercept

Interaction

Normal

None

If a line passes through points $(4,3)$ and $(2,\lambda)$ will be shifted into;

$(-2,1)$

$(0,-2)$

$(-2,-2)$

$(2,2)$

None

Equation of line having slope 3 making x-intercept 5 is

$x+\frac{1}{3}y-5=0$

$-3x+y+15=0$

$3x-y+5=0$

$y=3x+5$

None

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