Chapter 4 | Introduction to Analytic Geometry | Entry Test Preparation

Welcome to your Chapter 4(Introduction to Analytical Geometry)

Name

Class

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

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

$a=\sqrt{2}b$

$b=-\sqrt{2}a$

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

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

None

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

$\frac{15}{10}$

$\frac{7}{2}$

$4$

$\frac{7}{10}$

None

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

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

$-3x+y+15=0$

$y=3x+5$

$3x-y+5=0$

None

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

$(-2,1)$

$(2,2)$

$(-2,-2)$

$(0,-2)$

None

The slope formula is given by;

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

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

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

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

None

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

slope

quadrants

vertices

Distance

None

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

$(-1,4)$

$(1,4)$

$(-4,1)$

$(-4,-1)$

None

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

$y+2x+7=0$

$3x+7y+20=0$

$4y+13x=19$

$2x-y+11=0$

None

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

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

$5y+3x=0$

$5y+3x-26=0$

$9x+2y+17$

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;

$8x+51y-35=0$

$23x-43y+27=0$

$x-13y+19=0$

$18x+29y-21=0$

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;

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

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

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

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

None

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

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

$px+qy+px_2+qy_2=0$

$px_2+qy_2=0$

$qx_2-py_2-qx+py=0$

None

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

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

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

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

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

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}$$\begin{bmatrix} x \\ y \\ 1 \end{bmatrix}$$=\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}$

$\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}$

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

None

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

$\sqrt{113}$

$\sqrt{65}$

$\sqrt{85}$

$\sqrt{117}$

None

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

$x+y=1$

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

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

$x+y=\sqrt{2}$

None

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 $\tan{\theta}$=______;

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

None of these

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

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

None

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

$y=mx+r$

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

None

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

None

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

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

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

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

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

None

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

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

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

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

None of these

None

The inclination of any line parallel to y-axis is

$\frac{\pi}{2}$

$0$

$\frac{\pi}{4}$

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

None

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

Slope-intercept

Interaction

Normal

point - Slope

None

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

$(17,9)$

$(-6,-1)$

$(6, -18)$

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

None

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

$\infty$

$0$

$1$

$2$

None

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

vertices of rectangle

Collinear

Vertices of $\triangle$

all

None

Slope of a line parallel to y-axis is;

$-1$

$1$

undefined

$0$

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 _______ ?

$(3, -3)$

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

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

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

None

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

$-\frac{11}{15}$

$17$

$\frac{20}{7}$

$20$

None

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

A right angled $\Delta$

An isosceles $\Delta$

An equilateral $\Delta$

A right angled isosceles $\Delta$

None

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

$(3,1)$

$(-4,-1)$

$(-3,-1)$

$(-3,1)$

None

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

$1:3$

$2:3$

$3:2$

$3:1$

None

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

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

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

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

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

None

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

$3:2$

$1:3$

$3:5$

$2:3$

None

The inclination of the x-axis is;

$180^{o}$

$0^{o}$

$90^{o}$

$150^{o}$

None

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

$\frac{13}{2}$

$2$

$12$

$\frac{59}{3}$

None

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

17 square units

68 square units

34 square units

7.5 square units

None

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

$67$

$56$

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

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

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;

$650$

$450$

$350$

$536$

None

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

line

quadratic equation

Triangle

rectangle

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

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