Latus Rectum

Q.

If the vertex of a parabola be at origin and directrix be x+5 = 0 , then its latus rectum is

1. 5

2. 10

3. 40

4. 20

Q. If (9, 12) is one end of a double ordinate of the parabola $y^2=16x$ then its equation is

1. x+9=0

2. y-9=0

3. x-9=0

4. y+9=0

Q.

Find the equation of the ellipse whose centre lies at the origin, major axis lies on the x-axis, the eccentricity is $\frac{2}{3}$ and the length of the latus rectum is 5 units.

Q.

The parabola x² + 2x - 4y = 0 has

1. Letus rectum = 4

2. Vertex = (-1, -1)

3. 

4. 

Q. The latus rectum of a parabola whose directrix is x + y – 2 = 0 and focus is (3, -4), is

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

Q.

The ends of latus rectum of parabola $x^2+8y=0$ are

1. (-4, -2) and (4, 2)

2. (4, -2) and (-4, 2)

3. (-4, -2) and (4, -2)

4. (4, 2) and (-4, 2)

Q.

The length of the latus rectum of the parabola $9x^2-6x+36y+19=0$

1. 36

2. 9

3. 6

4. 4

Q. If the curve $y=|x-3|$ touches the parabola $y^2=\lambda (x-4),\lambda >0,$ then length of latus rectum of the parabola(in units) is

1. $2$
2. $4$
3. $16$
4. $8$

Q.

A parabola passing through the point (-4, -2) has its vertex at the origin and y-axis as its axis. The latus rectum of

the parabola is

1. 6

2. 8

3. 10

4. 12

Q. If three points A (h, 0), P (a, b) and B (0, k) lie on a line, show that: $\frac{a}{h}+\frac{b}{k}=1$.

Q. If P is any point on the hyperbola whose axis are equal, prove that SP. SP = CP².