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Recent questions tagged straight-lines

Find the equation of the lines which passes through the point (3, 4) and cuts off intercepts from the coordinate axes such that their sum is 14.

asked Jun 30, 2014 by thanvigandhi_1

1 answer

Find the angle between the lines $y = (2 – \sqrt3 ) (x + 5)$ and $y = (2 + \sqrt3 ) (x – 7).$

asked Jun 30, 2014 by thanvigandhi_1

1 answer

Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, – 1)

asked Jun 30, 2014 by thanvigandhi_1

1 answer

Find the equation of the straight line which passes through the point (1, – 2) and cuts off equal intercepts from axes

asked Jun 30, 2014 by thanvigandhi_1

1 answer

A person standing at the junction (crossing) of two straight paths represented by the equations $2x – 3y + 4 = 0$ and $3x + 4y – 5 = 0 $ wants to reach the path whose equation is $6x – 7y + 8 = 0$ in the least time. Find equation of the path that he should follow.

asked May 23, 2014 by thanvigandhi_1

1 answer

Prove that the product of the lengths of the perpendiculars drawn from the points $ ( \sqrt{a^2-b^2}, 0)$ and $ ( -\sqrt{a^2-b^2}, 0)$ to the line $ \large\frac{x}{a}$$ \cos \theta + \large\frac{y}{b}$$ \sin \theta = 1$ is $b^2$

asked May 23, 2014 by thanvigandhi_1

1 answer

A ray of light passing through the point (1, 2) reflects on the $x$ - axis at point $A$ and the reflected ray passes through the point (5, 3). Find the coordinates of $A$

asked May 23, 2014 by thanvigandhi_1

1 answer

Find equation of the line which is equidistant from parallel lines $9x + 6y – 7 = 0$ and $3x + 2y + 6 = 0.$

asked May 23, 2014 by thanvigandhi_1

1 answer

If sum of the perpendicular distances of a variable point $P (x, y)$ from the lines $ x + y – 5 = 0$ and $3x – 2y +7 = 0$ is always 10. Show that $ P$ must move on a line

asked May 22, 2014 by thanvigandhi_1

1 answer

If the lines $ y = 3x +1$ and $2y = x + 3$ are equally inclined to the line $y = mx + 4$, find the value of $m$.

asked May 22, 2014 by thanvigandhi_1

1 answer

Find the image of the point (3, 8) with respect to the line $x +3y = 7$ assuming the line to be a plane mirror

asked May 21, 2014 by thanvigandhi_1

1 answer

Find the direction in which a straight line must be drawn through the point (–1, 2) so that its point of intersection with the line $ x + y = 4$ may be at a distance of 3 units from this point

asked May 21, 2014 by thanvigandhi_1

1 answer

Find the distance of the line $4x + 7y + 5 = 0$ from the point (1, 2) along the line $2x-y=0$

asked May 21, 2014 by thanvigandhi_1

1 answer

In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?

asked May 21, 2014 by thanvigandhi_1

1 answer

Show that the equation of the line passing through the origin and making an angle $ \theta $ with the line $y=mx+c$ is $ \large\frac{y}{x}$$ = \large\frac{m \pm \tan \theta}{1 \mp m \tan \theta}$

asked May 21, 2014 by thanvigandhi_1

1 answer

Find the equation of the line passing through the point of intersection of the lines $4x + 7y – 3 = 0$ and $2x – 3y + 1 = 0$ that has equal intercepts on the axes.

asked May 21, 2014 by thanvigandhi_1

1 answer

Find the equation of the lines through the point (3, 2) which make an angle of $45^{\circ}$ with the line $x-2y=3.$

asked May 20, 2014 by thanvigandhi_1

1 answer

If three lines whose equations are $y = m_1, x+ c_1, y = m_2, x+c_2$ and $y = m_3, x+c_3$ are concurrent, then show that $m_1(c_2-c_3)+m_2(c_3-c_1)+m_3(c_1-c_2)=0$

asked May 20, 2014 by thanvigandhi_1

1 answer

Find the value of $p$ so that the three lines $3x + y – 2 = 0, px + 2 y – 3 = 0$ and $2x – y – 3 = 0$ may intersect at one point.

asked May 20, 2014 by thanvigandhi_1

1 answer

Find the area of the triangle formed by the lines $y – x = \theta, x + y = \theta$ and $x – k = \theta$

asked May 20, 2014 by thanvigandhi_1

1 answer

Find the equation of a line drawn perpendicular to the line $ \large\frac{x}{4}$$+\large\frac{y}{6}$$=1$ through the point, where it meets the $y$ - axis

asked May 20, 2014 by thanvigandhi_1

1 answer

Find the equation of the line parallel to $y$ - axis and drawn through the point of intersection of the lines $x – 7y + 5 = 0$ and $3x + y = \theta.$

asked May 20, 2014 by thanvigandhi_1

1 answer

Find perpendicular distance from the origin to the line joining the points $ (\cos \theta, \sin \theta) $ and $(\cos \phi, \sin \phi)$

asked May 20, 2014 by thanvigandhi_1

1 answer

What are the points on the $y$ - axis whose distance from the line $ \large\frac{x}{3}$$+ \large\frac{y}{4}$$=1$ is 4 units.

asked May 18, 2014 by thanvigandhi_1

1 answer

Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and – 6, respectively

asked May 18, 2014 by thanvigandhi_1

1 answer

Find the values of $ \theta$ and $p$, if the equation $x\: \cos \theta + y \sin \theta = p$ is the normal form of the line $ \sqrt 3 x+y+2=0.$

asked May 18, 2014 by thanvigandhi_1

1 answer

Find the values of $k$ for which the line $(k-3)x-(4-k^2)y+k^2-7k+6=0$ is passing through the origin.

asked May 18, 2014 by thanvigandhi_1

1 answer

Find the values of $k$ for which the line $(k-3)x-(4-k^2)y+k^2-7k+6=0$ is Parallel to the $y$ axis.

asked May 18, 2014 by thanvigandhi_1

1 answer

Find the values of $k$ for which the line $(k-3)x-(4-k^2)y+k^2-7k+6=0$ is Parallel to the $x$ axis.

asked May 18, 2014 by thanvigandhi_1

1 answer

If $p$ is the length of perpendicular from the origin to the line whose intercepts on the axes are $a$ and $b$, then show that $ \large\frac{1}{p^2}$$= \large\frac{1}{a^2}$$ +\large\frac{1}{b^2}$

asked May 18, 2014 by thanvigandhi_1

1 answer

In the triangle ABC with vertices A(2,3), B(4,-1) and C(1,2), find the equation and length of altitude from the vertex A.

asked May 14, 2014 by thanvigandhi_1

1 answer

If $p$ and $q$ are the lengths of perpendiculars from the origin to the lines $ x \cos \theta - y \sin \theta = k \cos 2\theta$ and $ x \sec \theta + y \: cosec \theta -k$, respectively, prove that $ p^2+4q^2=k^2$

asked May 13, 2014 by thanvigandhi_1

1 answer

The perpendicular from the origin to the line $y=mx+c$ meets it at the point (-1,2). Find the values of $m$ and $c$.

asked May 13, 2014 by thanvigandhi_1

1 answer

Find the coordinates of the foot of perpendicular from the point (-1,3) to the line $3x-4y-16=0$

asked May 13, 2014 by thanvigandhi_1

1 answer

Find the equation of the right bisector of the line segment joining the points (3,4) and (-1,2)

asked May 13, 2014 by thanvigandhi_1

1 answer

Two lines passing through the point (2,3) intersects each other at an angle of $60^{\circ}$. If slope of one line is 2, find equation of the other line.

asked May 13, 2014 by thanvigandhi_1

1 answer

Prove that the line through the point $(x_1, y_1)$ and parallel to the line $Ax+By+C=0$ is \[\] $\qquad \qquad A(x-x_1)+B(y-y_1)=0$.

asked May 13, 2014 by thanvigandhi_1

1 answer

The line through the points $(h,3)$ and $(4,1)$ intersects the line $7x-9y-19=0$ at right angle. Find the value of $h$.

asked May 10, 2014 by thanvigandhi_1

1 answer

Find angles between the lines $ \sqrt 3x+y=1$ and $x+\sqrt 3y=1$.

asked May 10, 2014 by thanvigandhi_1

1 answer

Find equation of the line perpendicular to the line $x-7y+5=0$ and having $x$ intercept 3.

asked May 10, 2014 by thanvigandhi_1

1 answer

Find the equation of the line parallel to the line $3x-4y+2=0$ and passing through the point $(-2, 3)$

asked May 10, 2014 by thanvigandhi_1

1 answer

Find the distance between parallel lines $ l(x+y)+p=0$ and $l(x+y)-r=0$.

asked May 9, 2014 by thanvigandhi_1

1 answer

Find the distance between parallel lines \[\] $15x+8y-34=0$ and $ 15x+8y+31=0$

asked May 9, 2014 by thanvigandhi_1

1 answer

Find the points on the $x$ axis, whose distance from the line $\large\frac{x}{3}$$+\large\frac{y}{4}$$=1$ are 4 units.

asked May 9, 2014 by thanvigandhi_1

1 answer

Find the distance of the point (-1, 1) from the line $12(x+6)=5(y-2)$.

asked May 9, 2014 by thanvigandhi_1

1 answer

Reduce the following equation into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive $x$ - axis. $ x-y=4$

asked May 7, 2014 by thanvigandhi_1

1 answer

Reduce the following equation into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive $x$ - axis. $ y-2=0$

asked May 7, 2014 by thanvigandhi_1

1 answer

Reduce the following equation into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive $x$ - axis. $ x-\sqrt 3 y +8=0$

asked May 7, 2014 by thanvigandhi_1

1 answer

Reduce the following equation into intercept form and find their intercepts on the axes $3y+2=0$

asked May 7, 2014 by thanvigandhi_1

1 answer

Reduce the following equation into intercept form and find their intercepts on the axes $4x-3y=6$

asked May 7, 2014 by thanvigandhi_1

1 answer

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