# Length of Latus Rectum

## Trending Questions

**Q.**

The length of the latus-rectum of the parabola x2−4x−8y+12=0 is

4

6

8

10

**Q.**The equation of the parabola whose focus is at (−1, −2) and the directrix is the line x−2y+3=0

- 4x2+y2+4xy+4x+32y+16=0
- 4x2+4y2+4xy+4x+32y+16=0
- 4x2+y2+4xy+2x+8y+16=0
- 4x2+y2+4xy+40x+16y+16=0

**Q.**The tangent PT and the normal PN to the parabola y2=4ax at a point P on it meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola, whose

- directrix is x = 0
- vertex is (2a3, 0)
- focus is (a, 0)
- latus rectum is 2a3

**Q.**

The length of the latus-rectum of the parabola y2+8x−2y+17=0 is

2

4

8

16

**Q.**

The length of the latus-rectum of the parabola 4y2+2x−20y+17=0

3

9

6

12

**Q.**The circle x2+y2+6x−24y+72=0 and hyperbola x2−y2+6x+16y=46 intersect at four distinct points. If these four points of intersection lie on a parabola, then

- the coordinates of the focus of the parabola is (−3, 2)
- the coordinates of the focus of the parabola is (−3, 0)
- the equation of the directrix of the parabola is y=0
- the length of the latus rectum of the parabola is 4.

**Q.**If a parabola passing through point (−4, −2) has its vertex at the origin and y−axis as its axis of symmetry, then the length of the latus rectum of the parabola is

**Q.**If C is a circle described on the focal chord of the parabola y2=4x as diameter which is inclined at an angle of 45∘ with the positive x−axis, then

- Radius of the circle is 2 units
- The centre of circle is (3, 2)
- The line x+1=0 touches the circle
- The circle x2+y2+2x−6y+3=0 is orthogonal to C

**Q.**

A parabola has the origin as its focus and the line $x=2$as the directrix. Then, the vertex of the parabola is at

$(2,0)$

$(0,2)$

$(1,0)$

$(0,1)$

**Q.**A beam is supported at its ends by two supports which are 12 m apart. Since the load is concentrated at its centre, there is a deflection of 3 cm at the centre and the deflected beam is in the shape of a parabola. Then distance from the centre where deflection is 1 cm, is

- 2√6
- 6
- 24
- √6

**Q.**

If $b$and $c$ are the lengths of the segments of any focal chord of a parabola ${y}^{2}=4ax$,

then the length of the latus rectum is$\phantom{\rule{0ex}{0ex}}$.

$\frac{bc}{\left[b+c\right]}$

$\sqrt{bc}$

$\frac{[b+c]}{2}$

$\frac{2bc}{\left[b+c\right]}$

**Q.**If the vertex of the parabola is (2, −3) and its directrix is 4x+3y+6=0, then the length of its latus rectum is

**Q.**If AFB is a focal chord of the parabola y2=4ax and AF = 4, FB = 5, then the latus-rectum of the parabola is equal to

**Q.**

Locus of all point $P\left(x,y\right)$ satisfy ${x}^{3}+{y}^{3}+3xy=1$ consist a union of

A line and an isolated point

A line pair and an isolated point

A line and a circle

A circle and an isolated point.

**Q.**If (2, 4) and (2, −4) are the end points of latus rectum, then which of the following can be vertex of parabola

- (0, 0)
- (2, 0)
- (4, 0)
- (10, 0)

**Q.**The length of the line segments joining focus to the point of intersection of angular bisector of co-ordinate axes (in the first quadrant) and the parabola y2=lx is

- l4
- 2l
- 5l4
- l√2

**Q.**If (2, 0) is vertex and y−axis is the directrix of a parabola. Then the length of its latus rectum is

- 2
- 4
- 8
- 16

**Q.**The angle made by the latus-rectum of the parabola y2=4ax at it's vertex is θ then 3∣∣∣tan(π4+θ2)+tan(π4−θ2)∣∣∣ is

**Q.**

Find the coordinates of the point of intersection of the axis and the directrix of the parabola whose focus is (3, 3) and directrix is 3x-4y=2.Find also the length of the latus-rectum.

**Q.**If y2+2y−x+5=0 represents a parabola, then the length (in units) of the latus rectum is

**Q.**The total number of focal chord(s) of length 167 in the parabola 7y2=8x is

**Q.**For the parabola x2+7y=0, which of the following is/are correct ?

- Equation of directrix is 4y−7=0
- Focus of the parabola is (0, 74)
- Length of latus-rectum is 7 units.
- End points of latus-rectum are (−72, −74) and (−72, 74)

**Q.**If PSQ is the focal chord of a parabola such that SP=2 and SQ=4 then the length of the latus rectum is

- 83
- 163
- 253
- 43

**Q.**If the vertex of the parabola is at origin and its directrix is x−3=0, then the length of its latus rectum is

**Q.**The circle x2+y2+6x−24y+72=0 and hyperbola x2−y2+6x+16y−46=0 intersect at four distinct points. These four points lie on a parabola, then

- the focus of parabola is (–3, 2)
- the vertex of parabola is (–3, 0)
- equation of directrix of parabola is y=0
- length of latus rectum of parabola is 4

**Q.**The length of the latus rectum of the parabola 3x2+4y+5+6x=0 is

- 13
- 23
- 53
- 43

**Q.**The length of the latus rectum of the parabola x=10y2+by+c, where b and c are constants, is 1k. Then k is equal to

**Q.**A beam is supported at its ends by two supports which are 12 m apart. Since the load is concentrated at its centre, there is a deflection of 3 cm at the centre and the deflected beam is in the shape of a parabola. Then distance from the centre where deflection is 1 cm, is

- 24
- √6
- 2√6
- 6

**Q.**

If b and c are lengths of the segments of any focal chord of the parabola y2=4ax, then write the lengths of its latus-rectum.

**Q.**Let PQ be a focal chord of the parabola y2=4x. The tangents to the parabola at P and Q meet at a point on

y = 2x + 1.

Length of chord PQ is

- 4
- 3
- 5
- 7