Recent questions tagged ch10

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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

A water tank is constructed on the top of a building with what speed will the water come out of a tank 8m below the water level the tank?Assume steady flow and that the pressure above the water level is equal to $P_{atm}$.

asked May 12, 2014 by sreemathi.v

1 answer

The profile of a dam is an arc of a circle,the arc having a radius of 30m and subtending an angle of $60^{\large\circ}$ at the centre of curvature which lies in the water surfaces.Determine the load on the dam in N/m

asked May 12, 2014 by sreemathi.v

1 answer

A tank with vertical sides is square in plane with 3m long sides.The tank contains oil of relative density 0.9 to a depth of 2.0m which is floating on water a depth of 1.5m.Calculate the force on the walls.(Consider one wall of the tank).

asked May 12, 2014 by sreemathi.v

1 answer

A closed tank has an orifice $0.025m$ diameter in one of its vertical sides.The tank contains oil to a depth of 0.61m above the centre of the orifice and the pressure in the air space above oil is maintained at $13780N/m^2$ above atmospheric.What is the discharge from the orifile.(Coefficient of discharge of the orifice is 0.61 relative density of oil is 0.9)

asked May 12, 2014 by sreemathi.v

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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

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

asked May 10, 2014 by thanvigandhi_1

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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

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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