ParabolaeasyFree

Find a if x+a=0 is Directrix of y²=2y+ax+2 | JEE Parabola

JEE Maths question with a full step-by-step solution.

Question
If x+a=0x + a = 0 is the directrix of the parabola y2=2y+ax+2y^2 = 2y + ax + 2, then the value of aa is:
A22correct
B33
C44
D43\dfrac{4}{3}
Solution
Step 1: Reduce to standard form.
y2−2y=ax+2⇒(y−1)2=a(x+3a).y^2 - 2y = ax + 2 \Rightarrow (y-1)^2 = a\left(x + \frac{3}{a}\right).
 This is (y−1)2=4A(x−h)(y-1)^2 = 4A(x-h) with 4A=a4A = a, so its directrix is x+3a+a4=0x + \dfrac{3}{a} + \dfrac{a}{4} = 0. Step 2: Match with the given directrix x+a=0x + a = 0.
3a+a4=a⇒12+a2=4a2⇒a2=4⇒a=2.\frac{3}{a} + \frac{a}{4} = a \Rightarrow 12 + a^2 = 4a^2 \Rightarrow a^2 = 4 \Rightarrow a = 2.
 Correct answer: (1)
Still stuck on this question?Ask your doubt on WhatsApp
Similar questions
Parabola · easy
The Cartesian equation of the curve whose parametric equations are x = t² + 2t + 3 and y…
Parabola · medium
The length of the latus rectum of the parabola x = t² + t + 1 , y = t² + 2t + 3 is:
Parabola · medium
If any point P(x, y) which satisfies the relation (5x - 1)² + (5y - 2)² = λ(3x - 4y - 1)²…
Parabola · medium
The locus of the vertex of the family of parabolas y = (a³ x²)/(3) + (a² x)/(2) - 2a , wh…

Solve more, learn faster

Sign up free to solve more JEE Maths questions and explore doMath — timed drills, mastery sprints, bookmarks, and chapter-wise progress tracking.

Sign up freeExplore doMath