Length of Latus Rectum
Trending Questions
Q.
Equation of the parabola with focus (3, -4) and directrix x+y+7=0
x2+y2-2xy-26x+2y+1=0
x2+y2-2xy-26x+14y-3=0
x2+y2-2xy-26x-14y+3=0
x2+y2-2xy-26x-2y+5=0
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.
Semi latus rectum of the parabola y2=4ax, is the _____ mean between segments of any focal chord of the parabola.
None of these
Arithmetic
Geometric
Harmonic
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. If y2+2y−x+5=0 represents a parabola, then the length (in units) of the latus rectum is
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. 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. 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. 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+y2+4xy+2x+8y+16=0
- 4x2+y2+4xy+40x+16y+16=0
- 4x2+4y2+4xy+4x+32y+16=0
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