Advertisements
Advertisements
प्रश्न
The equation of the line joining the point (3, 5) to the point of intersection of the lines 4x + y – 1 = 0 and 7x – 3y – 35 = 0 is equidistant from the points (0, 0) and (8, 34).
पर्याय
True
False
Advertisements
उत्तर
This statement is True.
Explanation:
Given equations are
4x + y – 1 = 0 ......(i)
And 7x – 3y – 35 = 0 ......(ii)
From equation (i) y = 1 – 4x ......(iii)
Putting the value of y in equation (ii) we get
7x – 3(1 – 4x) – 35 = 0
⇒ 7x – 3 + 12x – 35 = 0
⇒ 19x – 38 = 0
⇒ x = 2
From equation (iii) we get,
y = 1 – 4 × 2
⇒ y = – 7
The point of intersection is (2, – 7).
Equation of line joining the point (3, 5) to the point (2, – 7) is
y – 5 = `(-7 - 5)/(2 - 3) (x - 3)`
⇒ y – 5 = 12(x – 3)
⇒ y – 5 = 12x – 36
⇒ 12x – y – 31 = 0 .......(iv)
Distance of equation (iv) from the point (0, 0)
= `|(-31)/sqrt((12)^2 + (-1)^2)|`
= `31/sqrt(145)`
Distance of equation (iv) from the point (8, 34) is
= `|(12 xx 8 - 34 - 31)/sqrt((12)^2 + (-1)^2)|`
= `|(96 - 65)/sqrt(145)|`
= `31/sqrt(145)`
APPEARS IN
संबंधित प्रश्न
Find the equation of the line parallel to x-axis and passing through (3, −5).
Find the equation of the line perpendicular to x-axis and having intercept − 2 on x-axis.
Find the equation of the line passing through (0, 0) with slope m.
Find the equation of the line passing through \[(2, 2\sqrt{3})\] and inclined with x-axis at an angle of 75°.
Find the equation of the straight line which divides the join of the points (2, 3) and (−5, 8) in the ratio 3 : 4 and is also perpendicular to it.
Find the equation of the straight lines passing through the following pair of point :
(at1, a/t1) and (at2, a/t2)
Find the equations of the medians of a triangle, the coordinates of whose vertices are (−1, 6), (−3, −9) and (5, −8).
By using the concept of equation of a line, prove that the three points (−2, −2), (8, 2) and (3, 0) are collinear.
Find the equation to the straight line which bisects the distance between the points (a, b), (a', b') and also bisects the distance between the points (−a, b) and (a', −b').
In what ratio is the line joining the points (2, 3) and (4, −5) divided by the line passing through the points (6, 8) and (−3, −2).
The length L (in centimeters) of a copper rod is a linear function of its celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C.
Find the equation to the straight line cutting off intercepts 3 and 2 from the axes.
Find the equation of the line which passes through the point (3, 4) and is such that the portion of it intercepted between the axes is divided by the point in the ratio 2:3.
Find the equation of the straight line which passes through the point (−3, 8) and cuts off positive intercepts on the coordinate axes whose sum is 7.
Find the equation of a line which passes through the point (22, −6) and is such that the intercept of x-axis exceeds the intercept of y-axis by 5.
Find the equation of the line, which passes through P (1, −7) and meets the axes at A and Brespectively so that 4 AP − 3 BP = 0.
Find the equations of the straight lines which pass through the origin and trisect the portion of the straight line 2x + 3y = 6 which is intercepted between the axes.
A line is such that its segment between the straight lines 5x − y − 4 = 0 and 3x + 4y − 4 = 0 is bisected at the point (1, 5). Obtain its equation.
Find the equation of the straight line passing through the point of intersection of the lines 5x − 6y − 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x − 5y + 11 = 0 .
Find the equation of the straight line through the point (α, β) and perpendicular to the line lx + my + n = 0.
Find the length of the perpendicular from the point (4, −7) to the line joining the origin and the point of intersection of the lines 2x − 3y + 14 = 0 and 5x + 4y − 7 = 0.
Two sides of an isosceles triangle are given by the equations 7x − y + 3 = 0 and x + y − 3 = 0 and its third side passes through the point (1, −10). Determine the equation of the third side.
The equation of the base of an equilateral triangle is x + y = 2 and its vertex is (2, −1). Find the length and equations of its sides.
Prove that the family of lines represented by x (1 + λ) + y (2 − λ) + 5 = 0, λ being arbitrary, pass through a fixed point. Also, find the fixed point.
Find the equation of the straight line which passes through the point of intersection of the lines 3x − y = 5 and x + 3y = 1 and makes equal and positive intercepts on the axes.
Find the equations of the lines through the point of intersection of the lines x − 3y + 1 = 0 and 2x + 5y − 9 = 0 and whose distance from the origin is \[\sqrt{5}\].
If a, b, c are in G.P. write the area of the triangle formed by the line ax + by + c = 0 with the coordinates axes.
Write the equation of the line passing through the point (1, −2) and cutting off equal intercepts from the axes.
A line passes through the point (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is
If the point (5, 2) bisects the intercept of a line between the axes, then its equation is
The equation of the line passing through (1, 5) and perpendicular to the line 3x − 5y + 7 = 0 is
Find the equation of lines passing through (1, 2) and making angle 30° with y-axis.
A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.
Find the equations of the lines through the point of intersection of the lines x – y + 1 = 0 and 2x – 3y + 5 = 0 and whose distance from the point (3, 2) is `7/5`
The equations of the lines which pass through the point (3, –2) and are inclined at 60° to the line `sqrt(3) x + y` = 1 is ______.
The straight line 5x + 4y = 0 passes through the point of intersection of the straight lines x + 2y – 10 = 0 and 2x + y + 5 = 0.
