# Directrix

## Trending Questions

**Q.**The equation of parabola, whose axis is parallel to y−axis and which passes through points (0, 2), (−1, 0) and (1, 6) is

- y=x2+3x−2
- x2+3y+2=0
- y=x2+3x+2
- y2+3x+2=0

**Q.**If the line x−1=0 is the directrix of the parabola y2−kx+8=0, then one of the values of k is

- 18
- 8
- 4
- 14

**Q.**

The coordinates of the foot of the perpendicular drawn from the point $(3,4)$ on the line $2x+y-7=0$ is

$\left(\frac{9}{5},\frac{17}{5}\right)$

$(1,5)$

$(-5,1)$

$(1,-5)$

**Q.**

If the coordinates of the vertex and the focus of a parabola are (-1, 1) and (2, 3) respectively, then the equation of its directrix is

none of these

3x+2y+14=0

3x+2y-25=0

2x-3y+10=0

**Q.**

The directrix of the parabola x2−4x−8y+12=0 is

x=1

y=-1

y=0

x=-1

**Q.**A line L passing through the focus of the parabola y2=4(x−1), intersects the parabola at two distinct points. If m be the slope of the line L, then

- m∈R−{0}
- −1<m<1
- m<−1 or m>1
- None of these

**Q.**

The equation of straight line passing through the points (a, b, c) and (a - b, b- c, c - a), is

**Q.**The equation of parabola whose latus rectum is the line segment joining the points (–3, 1), (1, 1) is

- (x+1)2=2y
- (x+1)2=4y
- (x−1)2=4y
- (x+1)2=4y

**Q.**If the focus of the parabola (y−β)2=4(x−α) always lies between the lines x+y=1 and x+y=3 then

- 0<α+β<3
- 0<α+β<2
- −1<α+β<2
- 1<α+β<3

**Q.**

The equation of the directrix of the parabola whose vertex and focus are (1, 4) and (2, 6)

x+3y=8

x+2y=4

x-y=3

2x+y=5

**Q.**

Let f(x)=x2−px+q, p is an odd positive integer and the roots of the equation f(x)=0 are two distinct prime numbers, if p+q=35, then the value of f(10)(∑10r=1f(r))−878 equal to

**Q.**

The equation of the directrix of a parabola $2{x}^{2}=14y$ is equal to

$y=\frac{-7}{4}$

$x=\frac{-7}{4}$

$y=\frac{7}{4}$

$x=\frac{7}{4}$

**Q.**The mirror image of the directrix of the parabola y2=4(x+1) in the line mirror x+2y=3 is

- x=−2
- 4y+3x=16
- 3x−4y+16=0
- none of these

**Q.**

If the vertex and focus of a parabola are (3, 6) and (4, 5) then the equation of its directrix is

x-y+7=0

x-y+9=0

x-y+5=0

x-y+3=0

**Q.**A parabola has the origin as its focus and the line x=4 as the directrix. Then the vertex of the parabola is at

- (0, 4)
- (2, 0)
- (0, 2)
- (4, 0)

**Q.**If the focus is (1, –1) and the directrix is the line x + 2y – 9 = 0, the vertex of the parabola is

- (2, 1)
- (1, –2)
- (2, –1)
- (1, 2)

**Q.**If x+k=0 is equation of directrix to parabola y2=8(x+1)then k =

- 1
- 2
- 3
- 4

**Q.**The equation of the directrix of the parabola whose vertex (3, 2) and focus (2, –1) is

- 2x + 6y – 24 = 0
- x – 3y – 19 = 0
- x + 3y – 19 = 0
- y - 2y – 9 = 0

**Q.**

Find the equation of the parabola, if

(i) the focus is at (-6, -6) and the vertex is at (-2, 2)

(ii) the focus is at (0, -3) and the vertex is at (0, 0)

(iii) the focus is at (0, -3) and the vertex is at (-1, -3)

(iv) the focus is at (a, 0) and the vertex is at (a', 0)

(v) the focus is at (0, 0) and vertex is at the intersection of the lines x+y=1 and x-y=3.

**Q.**If the line 3x+4y=7 is a normal at a point P=(x1, y1) of the hyperbola 3x2−4y2=1, then the distance of P from the origin is

- √31912
- √33712
- √42312
- √52712

**Q.**

f(x)=x2+5x+6 defined on f: R → R is a many one function.

True

False

**Q.**

If the coordinates if the vertex and focus of a parabola re (-1, 1) and (2, 3) respectively, then write the equation of its directrix.

**Q.**The order of differential equation of all the parabolas whose axis is along positive x axis and vertex is at origin is

- 1
- 2
- 3
- not defined

**Q.**

The locus of a point whose chord of contact with respect to parabola

y2 = 8x passes through focus is

x + 2 = 0

Directrix of the given parabola

x + 1 = 0

Latus ractum of the given parabola

**Q.**

What is standard form for an ellipse?

**Q.**Find the equation to the line passing through the point (1, -2, -3) and parallel to the line 2x+3y-3z+2=0=3x-4y+2z-4.

**Q.**The coordinates of a point on the parabola y2=8x whose distance from the circle x2+(y+6)2=1 is minimum is

- (2, 4)
- (18, −12)
- (8, 8)
- (2, −4)

**Q.**Area of the segment cut off from the parabola x2=8y by the line x−2y+8=0 is:

- 12
- 24
- 48
- 36

**Q.**

The locus of a point whose chord of contact with respect to parabola

y2 = 8x passes through focus is

x + 2 = 0

Directrix of the given parabola

x + 1 = 0

Latus ractum of the given parabola

**Q.**If the line x−1=0 is the directrix of the parabola y2−kx+8=0, then values of k are

- 18
- −8
- 4
- 14