Length of Latus Rectum
Trending Questions
Q.
Semi latus rectum of the parabola y2=4ax, is the _____ mean between segments of any focal chord of the parabola.
Arithmetic
Geometric
Harmonic
None of these
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. 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. 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
- vertex is (2a3, 0)
- directrix is x = 0
- latus rectum is 2a3
- focus is (a, 0)
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. 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 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 curve for which the normal at any point P(x, y) and the line joining origin to the point P form an isosceles triangle with x−axis as base is
- A rectangular hyperbola
- An ellipse
- A parabola
- A circle
Q.
Semi latus rectum of the parabola y2=4ax, is the _____ mean between segments of any focal chord of the parabola.
Arithmetic
Geometric
Harmonic
None of these
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 curve for which the normal at any point P(x, y) and the line joining origin to the point P form an isosceles triangle with x−axis as base is
- An ellipse
- A parabola
- A rectangular hyperbola
- A circle
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
- vertex is (2a3, 0)
- directrix is x = 0
- latus rectum is 2a3
- focus is (a, 0)
Q. The lengths of the latus rectum of the parabolas
y2=12x and x2=−12y are equal.
y2=12x and x2=−12y are equal.
- False
- True
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. 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. Which of the following is incorrect regarding Latus rectum of a rectangular hyperbola?
- It is perpendicular to y=x
- There can be infinte number of focal chord and latus rectum in a hyperbola.
- There can be infinite number of focal chord but only two latus rectum in a hyperbola.
- It passes through focus.