# Pair of Lines

## Trending Questions

**Q.**

The equation $4{x}^{2}+12xy+9{y}^{2}+2gx+2fy+c=0$ will represent two real parallel straight lines if

$g=4,f=9,c=0$

$g=2,f=3,c=1$

$g=2,f=3,c$ is any number

$g=4,f=9,c>1$

**Q.**

Pair of straight lines perpendicular to each other represented by

$2{x}^{2}=2y(2x+y)$

${x}^{2}+{y}^{2}+3=0$

$2{x}^{2}=y(2x+y)$

${x}^{2}=2(x\u2013y)$

**Q.**Let ABC be a triangle with A(−3, 1) and ∠ACB=θ, 0<θ<π2. If the equation of the median through B is 2x+y−3=0 and the equation of angle bisector of C is 7x−4y−1=0, then tanθ is equal to

- 2
- 34
- 43
- 12

**Q.**If 2x2+7xy+3y2+8x+14y+λ=0 represents a pair of straight lines, then the value of λ is

**Q.**Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax+2ay+c=0 and 5bx+2by+d=0 lies in the fourth quadrant and is equidistant from the two axes then:

- 2bc−3ad=0
- 2bc+3ad=0
- 3bc−2ad=0
- 3bc+2ad=0

**Q.**

The angle between the lines represented by the equation $\lambda {x}^{2}+{\left(1-\lambda \right)}^{2}xy-\lambda {y}^{2}=0$ is

$30\xb0$

$45\xb0$

$60\xb0$

$90\xb0$

**Q.**

The curve y = ax^{3} + bx^{2} + cx + 5 touches the x-axis at P(-2, 0) and cuts the y-axis at the point Q where its gradient is 3. the equation of the curve is... .

**Q.**Find the equations of the lines parallel to axes and passing through (–2, 3).

**Q.**The angle between the lines 3x + 2y + z = 0 = x + y – 2z and 2x – y – z = 0 = 7x + 10y – 8z is :

- π6
- π2
- π3
- 0

**Q.**The equations x−y=4 and x2+4xy+y2=0 represent the sides of

- an equilateral triangle
- a right angled triangle
- an isosceles triangle
- a right angled isosceles triangle

**Q.**If the adjacent sides of a parallelogram are represented by 2x2−5xy+3y2=0 and the equation of one diagonal is x+y−2=0, then the equation of the other diagonal is

- 11x+9y=0
- 9x+11y=0
- 9x−11y=0
- 11x−9y=0

**Q.**The distance between the pair of parallel lines represented by x2+4xy+4y2+3x+6y−4=0 is ___ units

- √5
- 3
- 1√3
- 1√5

**Q.**The combined equation of two sides of a triangle is x2−3y2−2xy+8y−4=0. The third side, which is variable always passes through the point (−5, −1). If the range of values of the slope of the third line such that the origin is an interior point of the triangle is (a, b), then the value of (a+1b) is

- 12
- 2
- 4
- 0

**Q.**

The lines (lx+my)2−3(mx−ly)2=0 and lx + my + n = 0 form

A right angled triangle

None of these

An isosceles triangle

An equilateral triangle

**Q.**Product of perpendicular distances drawn from origin to pair of straight lines 12x2+25xy+12y2+10x+11y+2=0 is __ sq. units

- 125
- 425
- 325
- 225

**Q.**

The distance between the pair of parallel lines ${x}^{2}+2xy+{y}^{2}-8ax-8ay-9{a}^{2}=0$ is

$2\sqrt{5}a$

$\sqrt{10}a$

$10a$

$5\sqrt{2}$

**Q.**The area enclosed by the quadrilateral formed by x2y2−9x2−25y2+225=0 is

- 60 sq.units
- 100 sq.units
- 30 sq.units
- 20 sq.units

**Q.**The condition to be imposed on β so that (0, β) lies on or inside the triangle having sides y + 3x + 2 = 0, 3y – 2x – 5 = 0 and 4y + x – 14 = 0 is

**Q.**Area bounded by the ellipse 2x2+3y2=1 is

- π√6
- 6π
- √6π
- π6

**Q.**The straight lines represented by (y−mx)2=a2(1+m2) and (y−nx)2=a2(1+n2) forms

(where mn≠−1 and m≠n)

- square
- rhombus
- rectangle
- trapezium

**Q.**

Find the
direction in which a straight line must be drawn through the point
(–1, 2) so that its point of intersection with the line *x*
+ *y* = 4 may be at a distance of 3 units from this point.

**Q.**

The differential equation of the family of curves $\mathrm{y}=\mathrm{\alpha cos}\left(\mathrm{x}+\mathrm{b}\right)$ is

$\left(\frac{{d}^{2}y}{d{x}^{2}}\right)-y=0$

$\left(\frac{{d}^{2}y}{d{x}^{2}}\right)+y=0$

$\left(\frac{{d}^{2}y}{d{x}^{2}}\right)+2y=0$

None of these

**Q.**

Find the
points on the *x*-axis, whose distances from the line
are
4 units.

**Q.**If y=mx bisects the angle between the lines y=x2(sin2θ+tan2θ)+2xycosθ+y2sec2θ=0 when θ=π3. If the value of m is a±√b4, then b−10a=?

**Q.**If area of quadrilateral formed by lines 2x2+3xy−2y2=0 and 2x2+3xy−2y2+3x+y+1=0 is A sq. units, then the value of 20A is

**Q.**If the straight lines joining the origin and the point of the intersection of the curve x2+12xy−y2+4x−2y+3=0 and x+ky−1=0 are equally inclined to x-axis then the value of k is

- 1
- −1
- 0
- −2

**Q.**Equation of a line which is parallel to the line common to the pair of lines given by 6x2−xy−12y2=0 and 15x2+14xy−8y2=0 and at a distance of 7 units from it, is

- 3x+4y=35
- 3x+4y+35=0
- 2x−3y=35
- 2x−3y+35=0

**Q.**

Find the equation of the line which passes through the point (–4, 3) with slope.

**Q.**Find the equation of the circle drawn on the intercept made by the line 3x+4y=12 between the coordinate axes as diameter

**Q.**The lines joining the origin to the point of intersection of 3x2+mxy−4x+1=0 and 2x+y−1=0 are at right angles. Then all possible values of m lie in the interval

- (1, 2]
- [1, 2]
- ϕ
- R