(c) Here if the line is going through (0, 0) which is the beginning fulfills the given condition of line. Β \[\left( \mathbf{k}\text{ }\text{ }\mathbf{3} \right)\text{ }\left( \mathbf{0}...
A person standing at the junction (crossing) of two straight paths represented by the equations 2x β 3y + 4 = 0 and 3x + 4y β 5 = 0 wants to reach the path whose equation is 6x β 7y + 8 = 0 in the least time. Find equation of the path that he should follow.
GIVEN: $2x-3y+4=0$...(i) $3x+4y-5=0$...(ii) $6x-7y+8=0$...(iii) Here the individual is remaining at the intersection of the ways addressed by lines (1) and (2). By settling conditions (1) and (2) we...
Prove:
The product of the lengths of the perpendiculars drawn from the points to the line . GIVEN: IT CAN BE WRITTEN AS: \[bx\text{ }cos\text{ }\theta \text{ }+\text{ }ay\text{ }sin\text{ }\theta \text{...
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.
Consider the directions of point An as (a, 0) Develop a line (AL) which is opposite to the x-pivot Here the point of occurrence is equivalent to point of reflection \[\angle BAL\text{ }=\angle...
Find equation of the line which is equidistant from parallel lines 9x + 6y β 7 = 0 and 3x + 2y + 6 = 0.
Here $9h+6k-7=3(3h+2k+6)$ or $9h+6k-7=3(3h+2k+6)$ $9h+6k-7=3(3h+2k+6)$ wonβt be possible since $9h+6k-7=3(3h+2k+6)$ By additional estimation$7=18$ (isn't right) We realize that $9h+6k-7=-3(3h+2k+6)$...
If sum of the perpendicular distances of a variable point P (x, y) from the lines x + y β 5 = 0 and 3x β 2y + 7 = 0 is always 10. Show that P must move on a line.
SIMILARLY, equation of line for any signs of \[\left( x\text{ }+\text{ }y\text{ }\text{ }5 \right)\] and \[\left( 3x-\text{ }\text{ }2y\text{ }+\text{ }7 \right)\] CAN BE FOUND THUS, POINT P MUST...
If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.
GIVEN: \[y\text{ }=\text{ }3x\text{ }+\text{ }1\text{ }\ldots \text{ }\left( 1 \right)\] \[2y\text{ }=\text{ }x\text{ }+\text{ }3\text{ }\ldots \text{ }\left( 2 \right)\] \[y\text{ }=\text{...
Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.
Given: \[x\text{ }+\text{ }3y\text{ }=\text{ }7\text{ }\ldots \text{ }..\text{ }\left( 1 \right)\] Think about B (a, b) as the picture of point A (3, 8) So line (1) is opposite bisector of AB. On...
The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (β4, 1). Find the equation of the legs (perpendicular sides) of the triangle.
Consider ABC as the right points triangle where $\angle C={{90}^{\circ }}$ Here endlessness such lines are available. m is the slant of AC So the slant of $BC=-1/m$ Condition of AC $y-3=m(x-1)$ By...
Find the direction in which a straight line must be drawn through the point (β1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point.
Think about \[y\text{ }=\text{ }mx\text{ }+\text{ }c\] as the line going through the point (- 1, 2) \[2\text{ }=\text{ }m\text{ }\left( -1 \right)\text{ }+\text{ }c\] So we get By additional...
Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x β y = 0.
Β given : \[2x\text{ }\text{ }y\text{ }=\text{ }0\text{ }\ldots \text{ }..\text{ }\left( 1 \right)\] \[4x\text{ }+\text{ }7y\text{ }+\text{ }5\text{ }=\text{ }0\text{ }\ldots \text{ }\left( 2...
In what ratio, the line joining (β1, 1) and (5, 7) is divided by the line x + y = 4?
By cross augmentation \[\text{ }k\text{ }+\text{ }5\text{ }=\text{ }1\text{ }+\text{ }k\] We get \[2k\text{ }=\text{ }4\] \[k\text{ }=\text{ }2\] Henceforth, the line joining the...
Show that the equation of the line passing through the origin and making an angle ΞΈ with the line y = mx + c is
Think about \[y\text{ }=\text{ }m1x\] as the situation of the line going through the ORIGIN
Find the equation of the line passing through the point of intersection of the lines 4x + 7y β 3 = 0 and 2x β 3y + 1 = 0 that has equal intercepts on the axes.
Consider the condition of the line having equivalent captures on the tomahawks as \[x/a\text{ }+\text{ }y/a\text{ }=\text{ }1\] It tends to be composed as \[x\text{ }+\text{ }y\text{ }=\text{...
Find the equation of the lines through the point (3, 2) which make an angle of 45Β° with the line x β2y = 3.
Think about m1 as the slant of the necessary line It tends to be composed as $$ \[y\text{ }=\text{ }1/2\text{ }x\text{ }\text{ }3/2\] which is of the structure \[y\text{ }=\text{ }mx\text{ }+\text{...
If three lines whose equations are y = m1x + c1, y = m2x + c2 and y = m3x + c3 are concurrent, then show that m1 (c2 β c3) + m2 (c3 β c1) + m3 (c1 β c2) = 0
It is provided that \[y\text{ }=\text{ }{{m}_{1}}x\text{ }+\text{ }{{c}_{1}}~\ldots ..\text{ }\left( 1 \right)\] \[y\text{ }=\text{ }m2x\text{ }+\text{ }c2\text{ }\ldots \text{ }..\text{ }\left( 2...
Find the value of p so that the three lines 3x + y β 2 = 0, px + 2y β 3 = 0 and 2x β y β 3 = 0 may intersect at one point.
It is given that \[3x\text{ }+\text{ }y\text{ }\text{ }2\text{ }=\text{ }0\text{ }\ldots \text{ }\left( 1 \right)\] \[px\text{ }+\text{ }2y\text{ }\text{ }3\text{ }=\text{ }0\text{ }\ldots \text{...
Find the area of the triangle formed by the lines y β x = 0, x + y = 0 and x β k = 0
It is given that \[y\text{ }\text{ }x\text{ }=\text{ }0\text{ }\ldots \text{ }\left( 1 \right)\] \[x\text{ }+\text{ }y\text{ }=\text{ }0\text{ }\ldots \text{ }\left( 2 \right)\] \[x\text{ }\text{...
Find the equation of a line drawn perpendicular to the line x/4 + y/6 = 1 through the point, where it meets the y-axis.
It is given that \[x/4\text{ }+\text{ }y/6\text{ }=\text{ }1\] We can compose it as \[3x\text{ }+\text{ }2y\text{ }\text{ }12\text{ }=\text{ }0\] So we get \[y\text{ }=\text{ }-\text{ }3/2\text{...
Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines x β 7y + 5 = 0 and 3x + y = 0.
Here the situation of any line corresponding to the y-pivot is of the structure Β \[\mathbf{x}\text{ }=\text{ }\mathbf{a}\text{ }\ldots \text{ }.\text{ }\left( \mathbf{1} \right)\] Two given lines...
Find the perpendicular distance from the origin to the line joining the points :
according to the ques
What are the points on the y-axis whose distance from the line x/3 + y/4 = 1 is 4 units?
Consider (0, b) as the point on the y-pivot whose separation from line \[\mathbf{x}/\mathbf{3}\text{ }+\text{ }\mathbf{y}/\mathbf{4}\text{ }=\text{ }\mathbf{1}\text{ }\mathbf{is}\text{...
Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and β6, respectively.
Consider the captures cut by the given lines on a and b axes Β \[\mathbf{a}\text{ }+\text{ }\mathbf{b}\text{ }=\text{ }\mathbf{1}\text{ }\ldots \text{ }\left( \mathbf{1} \right)\]...
Find the values of ΞΈ and p, if the equation x cos ΞΈ + y sin ΞΈ = p is the normal form of the line β3x + y + 2 = 0.
according to the ques,
Find the values of k for which the line (k β 3) x β (4 β k2) y + k2 β 7k + 6 = 0 is (a) Parallel to the x-axis, (b) Parallel to the y-axis,
(a) Here if the line is corresponding to the x-pivot Β Slant of the line = Slope of the x-pivot Β It very well may be composed as Β \[\left( \mathbf{4}\text{ }\text{ }\mathbf{k2} \right)\text{...