Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

BITSAT 2023Paper 1

Exam: BITSAT
Year: 2023
Paper: Paper 1
Subject: Mathematics
Chapter: Parabola

BITSAT 2023 · Paper 1 · Mathematics · Parabola

The equation of a common tangent to the parabolas y=x^2 and...

The equation of a common tangent to the parabolas

y=x^2

and

y=-(x-2)^2

is

Options

A $y=4(x-2)$
B $y=4(x-1)$
C $y=4(x+1)$
D $y=4(x+2)$

Correct answer

B. $y=4(x-1)$

Step-by-step solution

Equation of tangent of parabola

y=x^2

be

t x=y+a t^2

...(i)

y=t x-\frac{t^2}{4}

Solve with

\mathrm{y}=-(\mathrm{x}-2)^2

t x-\frac{t^2}{4}=-(x-2)^2

x^2+x(t-4)-\frac{t^2}{4}+4=0

Here, Discriminant

=0

.

(t-4)^2-4 \cdot\left(4-\frac{t^2}{4}\right)=0 \Rightarrow t^2-4 t=0 \Rightarrow t=0

or

\mathrm{t}=4

Put value of

t

in eq. (i), then

y=4(x-1)

.

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 2024 Let 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 2024 If vertex of a parabola is (2,-1) and the equation of its directrix is 4 x-3 y=21 , then… BITSAT 2023 If the straight line y=m x+c touches the parabola y^2-4 a x+4 a^3=0 , then c is BITSAT 2022 A normal is drawn at the point P to the parabola y^2=8 x , which is inclined at 60^ ^ ∘… BITSAT 2022 The length of the latus rectum of the parabola which has focus at (-1,1) and the… BITSAT 2020 Suppose a parabola y = ax^ 2 + bx + c has two x intercepts, one positive and one… BITSAT 2019 Normals drawn to y ^ 2 = 4ax at the points where it is intersected by the line y = mx + c… BITSAT 2018 The locus of the point of intersection of two tangents to the parabola y^ 2 =4 a x, which… BITSAT 2016 The parabola having its focus at (3,2) and directrix along the y -axis has its vertex at BITSAT 2016 Let S be the focus of the parabola ^ 2 =8 x and PQ be the common chord of the circle ^ 2… BITSAT 2015 Through the vertex O of a parabola ^ 2 =4 x , chords OP and O Q are drawn at right angles… BITSAT 2014 If the line 2 x-3 y=k touches the parabola ^ 2 =6 x, then find the value of k BITSAT 2013 The length of the latus-rectum of the parabola whose focus is ((u^2)/(2 g) 2 α,-(u^2)/(2… BITSAT 2011 If the equations of the pairs of opposite sides of a parallelogram are x²-5 x+6=0 and… BITSAT 2010 The 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 PYQs JEE Mathematics PYQs All BITSAT PYQs