# Intercept of a Straight Line

## Trending Questions

**Q.**Slope of a line which cuts intercepts of equal lengths on the axes is

- −1
- 0
- 2
- √3

**Q.**The area (in sq. units) of the triangle formed by the coordinate axes and the line x(tanθ)+y(cotθ)=4 where θ∈(0, π2), is

**Q.**Let the line xa+yb=1 where ab>0, passes through P(α, β), where αβ>0. If the area formed by the line and the coordinate axes is S, then the least value of S is

- αβ
- 4αβ
- 2αβ
- αβ2

**Q.**If a, c, b are in G.P. and the area formed by the coordinate axes and the line ax+by+c=0 is A sq. units, then the value of 4A is

**Q.**A straight line through origin O meets the lines 3y=10−4x and 8x+6y+5=0 at points A and B respectively. Then O divides the segment AB in the ratio:

- 4:1
- 3:4
- 2:3
- 1:2

**Q.**The equation of the straight line which passes through the point P(−4, 3) such that the portion of it between the x-axis and y-axis is divided by the point P in the ratio 1:2 respectively, is

- x6−y9=1
- x9−y6=1
- y9−x6=1
- y9+x6=1

**Q.**

Find the equation of the straight line passing through the point of intersection of 2x+y−1=0 and x+3y−2=0 and making with the coordinate axes a triangle of area 38 sq. units.

**Q.**

The equation of the plane which is parallel to y-axis and cuts off intercepts of length 2 and 3 from x-axis and z-axis is

**Q.**Find the equation of the line which is passing through the point (–4, 3) with slope 12.

**Q.**

Find the equation of a line passing through the point $\left(2,4\right)$ and intersecting the line $2x+3y+6=0$ on the $X-axis$.

**Q.**If the X−coordinate of a point ′P′ on the segment joining Q(2, 2, 1) and R(5, 1, −2) is 4, then Z− coordinate is:

- −1
- 0
- 1
- 2

**Q.**True or false : If complex numbers Z1, Z2 and Z3 represent the vertices of an equilateral triangle such that |Z1|=|Z2|=|Z3|, then Z1+Z2+Z3=0.

**Q.**The equation of the plane through (1, 2, −3) and (2, −2, 1) and parallel to X− axis is

- y−z+1=0
- y−z−1=0
- y+z−1=0
- y+z+1=0

**Q.**Match List I with the List II and select the correct answer using the code given below the lists :

Let the line L:ax+by+c=0 intersect x−axis at A and y−axis at B. Let O be the origin.

List IList II(I)If a, b, c are in G.P. with common ratio as 2, then area of ΔAOB is(P)6(II)If a=1, b=1, c=2 and circumradius of ΔAOB is √p, p>0, then the value of 3p is(Q)4(III)If a=b=c=1 and reflection of O along the line L is (α, β), then |α+β| is (R)2(IV)If a=b=1, c=√2 and d is the shortest distance of line L from O, then 2d is (S)3(T)1

Which of the following is CORRECT combination?

- (I)→(R); (II)→(S); (III)→(Q); (IV)→(P)
- (I)→(Q); (II)→(T); (III)→(P) (IV)→(R)
- (I)→(Q); (II)→(T); (III)→(S); (IV)→(R)
- (I)→(Q); (II)→(P); (III)→(R); (IV)→(R)

**Q.**The area enclosed by 2|x|+3|y|≤6 is

- 3 sq. units
- 4 sq. units
- 12 sq. units
- 24 sq. units

**Q.**

ax + by = ab is the equation of a straight line which makes intercepts a & b on x & y axis respectively. State True or False.

True

False

**Q.**The number of arrangements of the letters of the word NAVA NAVA LAVANYAM which begin with N and end with M is

**Q.**The equation of the straight line which passes through the point (1, - 2) and cuts off equal intercepts from axes, is

- x+y=1
- x-y=1
- x+y+1=0
- x-y-2=0

**Q.**If a line parallel to 2x+6y−7=0 makes an intercept of 10 units between the coordinate axes and y− intercept is ±√k, then the value of k is

**Q.**The straight line passing through the point of intersection of the straight lines

x−3y+1=0 and 2x+5y−9=0

and having infinite slope and and at a distance 2 units from the origin has the equation

- x=2
- 3x+y−1=0
- y=1
- None of these

**Q.**The equation of line passing through (3, 4) and parallel to 5x+9y+12=0 is

- 5x−9y+51=0
- 5x−9y−51=0
- 5x+9y+51=0
- 5x+9y−51=0

**Q.**In a right angled isosceles △ABC, where A is at origin and side lengths AB and AC are equal to a units. If point B and C are produced to P and Q respectively such that BP⋅CQ=AB2, then the locus of the midpoint of PQ is

- 1x+1y=4a
- 1x+1y=12a
- 1x+1y=1a
- 1x+1y=2a

**Q.**If area enclosed by the simultaneous inequations x−2y2≥0 and 1−x−|y|≥0 is A sq. units, then the value of 12A is

**Q.**If a line parallel to 2x+6y−7=0 makes an intercept of 10 units between the coordinate axes and y− intercept is ±√k, then the value of k is

**Q.**Find the equation of a line having the angle of inclination 45∘ and y− intercept 2

**Q.**The two lines x=ay+b, z=cy+d and x=a′y+b′, z=c′y+d′ are perpendicular to each other if

- aa′+cc′=−1
- aa′+cc′=1
- aa′+cc′=1
- aa′+cc′=−1

**Q.**At what point, the slope of the curve y=−x3+3x2+9x−27 is maximum? Also find the maximum slope

**Q.**

Find the equation of the plane through the intersection of the planes →r.(^i+3^j)−6=0 and →r.(3^i−^j)−4^k=0, whose perpendicular distance from origin is unity.

**Q.**

The equation of the line joining origin to the points of intersection of the curve x2+y2=a2 and x2+y2−ax−ay=0 is

**Q.**The equation of line passing through (3, 4) and parallel to 5x+9y+12=0 is

- 5x−9y+51=0
- 5x−9y−51=0
- 5x+9y+51=0
- 5x+9y−51=0