Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2023Paper 2
Exam
BITSAT
Year
2023
Paper
Paper 2
Subject
Mathematics
Chapter
Parabola

BITSAT 2023 · Paper 2 · Mathematics · Parabola

If vertex of a parabola is (2,-1) and the equation of its directrix...

If vertex of a parabola is (2,−1)(2,-1) and the equation of its directrix is 4x−3y=214 x-3 y=21, then the length of its latus rectum isIf vertex of a parabola is (2,-1) and the equation of its directrix is 4 x-3 y=21 , then the length of its latus rectum

Options

  1. A
    2
  2. B
    8
  3. C
    12
  4. D
    16

Correct answer

B.
8

Step-by-step solution


If vertex of a parabola is (2,-1) and the equation of its directrix is 4 x-3 y=21 , then the length of its latus rectum

We are given that directrix of the parabola is 4x−3y=214 x-3 y=21 and vertex of the parabola is (2,−1)(2,-1)
Now a=∣8+3−21∣5=105=2a=\frac{|8+3-21|}{5}=\frac{10}{5}=2
∴\therefore \quad latus rectum of the parabola =4a=8=4 a=8
Practice Parabola on Quantrex Academy →

More from Parabola

If the focus of parabola (y-k)^2=4(x-h) always lies between the lines x+y=1 and x+y=3 then BITSAT 2024Let L_1 be the length of the common chord of the curves x^2+y^2=9 and y^2=8 x , and L_2… BITSAT 2024The equation of a common tangent to the parabolas y=x^2 and y=-(x-2)^2 is BITSAT 2023If the straight line y=m x+c touches the parabola y^2-4 a x+4 a^3=0 , then c is BITSAT 2022A normal is drawn at the point P to the parabola y^2=8 x , which is inclined at 60^ ^ ∘… BITSAT 2022The length of the latus rectum of the parabola which has focus at (-1,1) and the… BITSAT 2020Suppose a parabola y = ax^ 2 + bx + c has two x intercepts, one positive and one… BITSAT 2019Normals drawn to y ^ 2 = 4ax at the points where it is intersected by the line y = mx + c… BITSAT 2018The locus of the point of intersection of two tangents to the parabola y^ 2 =4 a x, which… BITSAT 2016The parabola having its focus at (3,2) and directrix along the y -axis has its vertex at BITSAT 2016Let S be the focus of the parabola ^ 2 =8 x and PQ be the common chord of the circle ^ 2… BITSAT 2015Through the vertex O of a parabola ^ 2 =4 x , chords OP and O Q are drawn at right angles… BITSAT 2014If the line 2 x-3 y=k touches the parabola ^ 2 =6 x, then find the value of k BITSAT 2013The length of the latus-rectum of the parabola whose focus is ((u^2)/(2 g) 2 α,-(u^2)/(2… BITSAT 2011If the equations of the pairs of opposite sides of a parallelogram are x²-5 x+6=0 and… BITSAT 2010The line 3 x-4 y+7=0 is rotated through an angle (π)/(4) in the clockwise direction about… BITSAT 2009 Full Parabola list Parabola JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs