# Parametric Form of a Straight Line

## Trending Questions

**Q.**A variable line L is drawn through O(0, 0) to meet the lines L1:x+2y−3=0 and L2:x+2y+4=0 at points M and N respectively. A point P is taken on line L such that 1OP2=1OM2+1ON2. Then the locus of P is

- x2+4y2=14425
- (x+2y)2=14425
- 4x2+y2=14425
- (x−2y)2=14425

**Q.**Parametric form of a straight line passing through (4, 5) and making an angle 60∘ with x-axis in the positive direction is

(where λ be any parameter)

- x=λ+4, y=√3λ+5
- x=√3λ−4, y=λ+5
- x=√3λ+4, y=λ+5
- x=λ−4, y=λ+5

**Q.**The parametric equation of the line is given by

x=−2+r√10; y=1+3r√10, then for the line

- x intercept is 73
- y intercept is 7
- slope is 3
- x intercept is −73

**Q.**The slope of a straight line passing through A(−2, 3) is −43. The point(s) on the line that are 10 units away from A is/are

- (8, 0)
- (−8, 11)
- (4, −5)
- (4, 11)

**Q.**

If one vertex of an equilateral triangle of side $a$ lies at the origin and the other lies on line $x-\sqrt{3}y=0$, then the co-ordinates of the third vertex are

**Q.**If the straight line drawn through the point P(√3, 2) and inclined at an angle of π6 with the positive direction of x−axis meets the line √3x−4y+8=0 at point Q, then the length of PQ is

**Q.**If the straight line through the point P(3, 4) makes an angle π6 with the x-axis and meets the line 3x+5y+1=0 at Q, then length of PQ is

- 30(3√3−5) units
- 30(√3−1) units
- √3−1 units
- 30 units

**Q.**The parallelism condition for two straight lines one of which is specified by the equation ax+by+c=0 the other being represented parametrically by x=αt+β, y=γt+δ is given by

- αγ−bα=0, β=δ=c=0
- aα−bγ=0, β=δ=0
- aα+bγ=0
- aγ=bα=0

**Q.**

Find the area of the region bounded by the ellipse x216+y29=1.

**Q.**

Find the distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to the line 3x - 4y + 8 = 0.

**Q.**

Find the distance of the line 2x + y = 3 from the point (-1, -3) in the direction of the line whose slope is 1.

**Q.**

A line passes through a point A (1, 2) and makes an makes an angle of 60∘ with the x-axis and intersects the line x + y = 6 at the point P. Find AP.

**Q.**A straight line L is drawn through the point A(2, 1) such that its point of intersection with x+y=9 is at a distance of 3√2 unit's from A. Then

- Inclination of L is π4
- Inclination of L is π6
- L cuts the x−axis at (1, 0)
- L passes through (5, 4)

**Q.**A line which passes through P(4, 5) and making an angle of 30∘ with positive direction of x−axis. Then coordinates of point which is at a distance 4 unit's from the line on either side of P, is

- (4+2√3, 7), (4−2√3, 3)
- (4−2√3, 7), (4+2√3, 3)
- (4−2√3, 7), (4+2√3, 7)
- (4+2√3, 3), (4+2√3, 7)

**Q.**Let S=(0, 2π)−{π2, 3π4, 3π2, 7π4}. Let y=y(x), x∈S be the solution curve of the differential equation dydx=11+sin2x, y(π4)=12. If the sum of abscissas of all the points of intersection of the curve y=y(x) with the curve y=√2sinx is kπ12, then k is equal to

**Q.**

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.

**Q.**The equation of the medians of a triangle formed by the lines x+y−6=0, x−3y−2=0 and 5x−3y+2=0, is

- x=2, x−9y−14=0 and 7x−9y+2=0
- x=2, x+9y−14=0 and 7x−9y−2=0
- x=2, x−9y−14=0 and 7x+9y+2=0
- x=2, x+9y+14=0 and x−9y−2=0

**Q.**

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.

**Q.**The slope of the straight line passing through A(3, 2) is 34. The coordinates of the points that are 5 units away from A are:

- (7, 5)
- (-1, -1)
- (-7, -5)
- (1, 1)

**Q.**

A line a drawn through A (4, -1) parallel to the line 3 x - 4 y + 1 = 0. Find the coordinates of the two points on this line which are at a distance of 5 units from A.

**Q.**The area bounded by the curve y=sinx and y=cosx in between x=0 and x=π2 is

- √2
- 2
- 2+√2
- 2−√2

**Q.**Let origin is one vertex of an equilateral triangle of side length a units. If other vertex lies on the line x−√3y=0 in the first quadrant, then the co-ordinates of third vertex is/are

- (0, −a)
- (0, a)
- (√3a2, −a2)
- (−√3a2, a2)

**Q.**

Sketch the region {(x, 0) : y = √4−x2 and X - axis. Find the area of the region using integration.

**Q.**

For all values of θ, the lines represented by the equation

(2 cos θ+3 sin θ)x+(3 cos θ−5 sin θ)y−(5 cos θ−2 sin θ)=0

pass through a fixed point

pass through the point (1, 1)

pass through a fixed point whose reflection in the line

x+y=√2 is(√2−1, √2−1)pass through the origin

**Q.**

Find the distance of the point (2, 5) from the line 3 x + y + 4 = 0 measured parallel to a line having slope 3/4.

**Q.**The equation(s) of angular bisector between the intersecting lines L1:x1=y2=z3 and L2:x−3=y−2=z−1 is/are

- y2=z3, x=0
- x+z=y=0
- x=y=z
- x1=z2, y=0

**Q.**The area of the part of the circle x2+y2=8a2 and the parabola y2=2ax through which positive X-axis passes is

- 4a2(3π+23)
- (a2(3π+2)3)

- 2a2(3π−23)
- (2a2(3π+2)3)

**Q.**

Find the equations to the straight lines passing through the point (2, 3) and inclined at an angle of 45∘ to the line 3x+y−5=0

**Q.**

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.

**Q.**A point on the line (x, y)=(−3+rcosπ6, 2+rsinπ6) which is at a distance of 2 units from the point (−3, 2) is

- (−3+√3, 3)
- (−3−√3, 1)
- (−3−√3, 3)
- (−3+√3, 1)