Directrix

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

1. $y=x^2+3x-2$
2. $x^2+3y+2=0$
3. $y=x^2+3x+2$
4. $y^2+3x+2=0$

Q. If the line $x-1=0$ is the directrix of the parabola $y^2-kx+8=0$, then one of the values of $k$ is

1. $\frac{1}{8}$
2. $8$
3. $4$
4. $\frac{1}{4}$

Q.

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

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

2. $(1,5)$

3. $(-5,1)$

4. $(1,-5)$

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

1. none of these

2. 3x+2y+14=0

3. 3x+2y-25=0

4. 2x-3y+10=0

Q.

The directrix of the parabola $x^2-4x-8y+12=0$ is

1. x=1

2. y=-1

3. y=0

4. x=-1

Q. A line $L$ passing through the focus of the parabola $y^2=4(x-1),$ intersects the parabola at two distinct points. If $m$ be the slope of the line $L,$ then

1. $m\in R-\left\{0\right\}$
2. $-1<m<1$
3. $m<-1$ or $m>1$
4. None of these

Q.

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

1. 

2. 

3. 

4. 

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

1. $(x+1{)}^2=2y$
2. $(x+1{)}^2=4y$
3. $(x-1{)}^2=4y$
4. $(x+1{)}^2=4y$

Q. If the focus of the parabola $(y-\beta {)}^2=4(x-\alpha )$ always lies between the lines $x+y=1$ and $x+y=3$ then

1. $0<\alpha +\beta <3$
2. $0<\alpha +\beta <2$
3. $-1<\alpha +\beta <2$
4. $1<\alpha +\beta <3$

Q.

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

1. x+3y=8

2. x+2y=4

3. x-y=3

4. 2x+y=5

Q.

Let $f\left(x\right)=x^2-px+q,$ p is an odd positive integer and the roots of the equation $f\left(x\right)=0$ are two distinct prime numbers, if $p+q=35$, then the value of $f\left(10\right)\left({\sum }_{r=1}^{10}f\right(r\left)\right)-878$ equal to ___

Q.

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

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

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

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

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

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

1. $x=-2$
2. $4y+3x=16$
3. $3x-4y+16=0$
4. 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

1. x-y+7=0

2. x-y+9=0

3. x-y+5=0

4. 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

1. $(0,4)$
2. $(2,0)$
3. $(0,2)$
4. $(4,0)$

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

1. (2, 1)
2. (1, –2)
3. (2, –1)
4. (1, 2)

Q. If x+k=0 is equation of directrix to parabola $y^2=8(x+1)$then k =

1. 1
2. 2
3. 3
4. 4

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

1. 2x + 6y – 24 = 0
2. x – 3y – 19 = 0
3. x + 3y – 19 = 0
4. 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 $P=(x_1,y_1)$ of the hyperbola $3x^2-4y^2=1,$ then the distance of $P$ from the origin is

1. $\frac{\sqrt{319}}{12}$
2. $\frac{\sqrt{337}}{12}$
3. $\frac{\sqrt{423}}{12}$
4. $\frac{\sqrt{527}}{12}$

Q.

$f\left(x\right)=x^2+5x+6$ defined on f: R $\to$ R is a many one function.

1. True

2. 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. $1$
2. $2$
3. $3$
4. not defined

Q.

The locus of a point whose chord of contact with respect to parabola
$y^2=8x$ passes through focus is

1. $x+2=0$

2. Directrix of the given parabola

3. $x+1=0$

4. 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 $y^2=8x$ whose distance from the circle $x^2+(y+6{)}^2=1$ is minimum is

1. $(2,4)$
2. $(18,-12)$
3. $(8,8)$
4. $(2,-4)$

Q. Area of the segment cut off from the parabola $x^2=8y$ by the line $x-2y+8=0$ is:

1. $12$
2. $24$
3. $48$
4. $36$

Q.

The locus of a point whose chord of contact with respect to parabola
$y^2=8x$ passes through focus is

1. $x+2=0$

2. Directrix of the given parabola

3. $x+1=0$

4. Latus ractum of the given parabola

Q. If the line $x-1=0$ is the directrix of the parabola $y^2-kx+8=0,$ then values of $k$ are

1. $\frac{1}{8}$
2. $-8$
3. $4$
4. $\frac{1}{4}$