Advertisements
Advertisements
प्रश्न
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.
विकल्प
True
False
Advertisements
उत्तर
This statement is True.
Explanation:
Given equations are x + 2y – 10 = 0 ......(i)
And 2x + y + 5 = 0 ......(ii)
From equation (i) x = 10 – 2y
Putting the value of x in equation (ii) we get
2(10 – 2y) + y + 5 = 0
⇒ 20 – 4y + y + 5 = 0
⇒ – 3y + 25 = 0
⇒ y = `25/3`
Putting the value of y in equation (iii) we get
x = `10 - 2(25/3)`
= `(30 - 50)/3`
= `(-20)/3`
∴ Point = `((-20)/3, 25/3)`
If the given line 5x + 4y = 0 passes through the point `((-20)/3, 25/3)`
`5((-20)/3) + 4(25/3)` = 0
⇒ `(-100)/3 + 100/3` = 0
⇒ 0 = 0 satisfied.
So, the given line passes through the point of intersection of the given lines.
APPEARS IN
संबंधित प्रश्न
Draw the lines x = − 3, x = 2, y = − 2, y = 3 and write the coordinates of the vertices of the square so formed.
Find the equation of a line equidistant from the lines y = 10 and y = − 2.
Find the equation of the straight line passing through the point (6, 2) and having slope − 3.
Find the equation of the line passing through (0, 0) with slope m.
Find the equation of the straight line passing through (3, −2) and making an angle of 60° with the positive direction of y-axis.
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 line passing through the point (−3, 5) and perpendicular to the line joining (2, 5) and (−3, 6).
Find the equation of the straight lines passing through the following pair of point :
(0, 0) and (2, −2)
The owner of a milk store finds that he can sell 980 litres milk each week at Rs 14 per liter and 1220 liters of milk each week at Rs 16 per liter. Assuming a linear relationship between selling price and demand, how many liters could he sell weekly at Rs 17 per liter.
Find the equation of the line which passes through the point (− 4, 3) and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point.
A straight line passes through the point (α, β) and this point bisects the portion of the line intercepted between the axes. Show that the equation of the straight line is \[\frac{x}{2 \alpha} + \frac{y}{2 \beta} = 1\].
Find the equations of the straight lines each of which passes through the point (3, 2) and cuts off intercepts a and b respectively on X and Y-axes such that a − b = 2.
A straight line drawn through the point A (2, 1) making an angle π/4 with positive x-axis intersects another line x + 2y + 1 = 0 in the point B. Find length AB.
The straight line through P (x1, y1) inclined at an angle θ with the x-axis meets the line ax + by + c = 0 in Q. Find the length of PQ.
Find the equation of straight line passing through (−2, −7) and having an intercept of length 3 between the straight lines 4x + 3y = 12 and 4x + 3y = 3.
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.
If the straight line \[\frac{x}{a} + \frac{y}{b} = 1\] passes through the point of intersection of the lines x + y = 3 and 2x − 3y = 1 and is parallel to x − y − 6 = 0, find a and b.
Find the equation of a line drawn perpendicular to the line \[\frac{x}{4} + \frac{y}{6} = 1\] through the point where it meets the y-axis.
Find the equations to the sides of an isosceles right angled triangle the equation of whose hypotenues is 3x + 4y = 4 and the opposite vertex is the point (2, 2).
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.
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 \[\sqrt{5}\].
Write the equation of the line passing through the point (1, −2) and cutting off equal intercepts from the axes.
Find the locus of the mid-points of the portion of the line x sinθ+ y cosθ = p intercepted between the axes.
The equation of the straight line which passes through the point (−4, 3) such that the portion of the line between the axes is divided internally by the point in the ratio 5 : 3 is
If a + b + c = 0, then the family of lines 3ax + by + 2c = 0 pass through fixed point
If the point (5, 2) bisects the intercept of a line between the axes, then its equation is
Find the equation of the line passing through the point of intersection of 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7.
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.
If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through ______.
The lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent if a, b, c are in G.P.
