Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main 201226 MayOnline

Exam: JEE Main
Year: 2012
Date: 26 May
Mode: Online
Subject: Mathematics
Chapter: Parabola

JEE Main 2012 · 26 May · Online · Mathematics · Parabola

The chord P Q of the parabola y^2=x , where one end P of the chord...

The chord

P Q

of the parabola

y^2=x

, where one end

P

of the chord is at point

(4,-2)

, is perpendicular to the axis of the parabola. Then the slope of the normal at

Q

is

The chord P Q of the parabola y^2=x , where one end P of the chord is at point (4,-2) , is perpendicular to the axis of

The chord P Q of the parabola y^2=x , where one end P of the chord is at point (4,-2) , is perpendicular to the axis of

Options

A $-4$
B $-\frac{1}{4}$
C4
D $\frac{1}{4}$

Correct answer

A. $-4$

Step-by-step solution

Point

P

is (4,-2)

and P Q \perp x

-axis So,

Q=(4,2)

The chord P Q of the parabola y^2=x , where one end P of the chord is at point (4,-2) , is perpendicular to the axis of

Equation of tangent at

(4,2)

is

\begin{aligned}& y y_1=\frac{1}{2}\left(x+x_1\right) \\ & \Rightarrow 2 y=\frac{1}{2}(x+2) \Rightarrow 4 y=x+2 \\ & \Rightarrow y=\frac{x}{4}+\frac{1}{2}\end{aligned}

So, slope

of tangent =

\frac{1}{4}

\therefore

Slope of normal $=-4

Practice Parabola on Quantrex Academy →

More from Parabola

Let T be the tangent to the parabola y^2 = 16x at the point (64, 32) . Let L be the… JEE Advanced 2026 Let O be the vertex of the parabola y^2=4x and its chords OP and OQ are perpendicular to… JEE Main 2026 Let chord PQ of length 3 13 of the parabola y^2 = 12x be such that the ordinates of… JEE Main 2026 Let the point P be the vertex of the parabola y = x^2 - 6x + 12 . If a line passing… JEE Main 2026 Let the directrix of the parabola P: y^2 = 8x , cut x -axis at the point A . Let B(α, β)… JEE Main 2026 Let A,B and C be the vertices of a variable right angled triangle inscribed in the… JEE Main 2026 Consider the parabola P : y^2 = 4kx and the ellipse E : (x^2)/(a^2) + (y^2)/(b^2) = 1 .… JEE Main 2026 Let the parabola y = x^2 + px + q passing through the point (1, -1) be such that the… JEE Main 2026 Let A be the focus of the parabola y^ 2 =8 x . Let the line y=m x+c intersect the… JEE Main 2026 Let the image of parabola x^ 2 =4 y , in the line x-y=1 be (y+a)^ 2 =b(x-c) , a, b, c ∈… JEE Main 2026 An equilateral triangle OAB is inscribed in the parabola y^ 2 =4 x with the vertex O at… JEE Main 2026 Let the locus of the mid-point of the chord through the origin O of the parabola y^ 2 =4… JEE Main 2026 If the chord joining the points P_ 1 (x_ 1 , y_ 1 ) and P_ 2 (x_ 2 , y_ 2 ) on the… JEE Main 2026 Let y^ 2 =12 x be the parabola with its vertex at O. Let P be a point on the parabola and… JEE Main 2026 Let one end of a focal chord of the parabola y^ 2 =16 x be (16,16) . If P(α, β) divides… JEE Main 2026 Let O be the vertex of the parabola x^ 2 =4 y and Q be any point on it. Let the locus of… JEE Main 2026 Full Parabola list Parabola JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs