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Mathematics · Parabola

JEE Main 2025 — 7 April, Morning Shift — Question 33

Let PP be the parabola, whose focus is (−2,1)(-2,1) and directrix is 2x+y+2=02 x+y+2=0. Then the sum of the ordinates of the points on PP, whose abscissa is -2 , is

  1. Option A:

    14\frac{1}{4}

  2. Option B:

    32\frac{3}{2}

    Correct
  3. Option C:

    34\frac{3}{4}

  4. Option D:

    52\frac{5}{2}

Answer: B

Step-by-step solution

PM=PFP M=P F

⇒∣2x+y+2∣5=(x+2)2+(y−1)2\Rightarrow \frac{|2 x+y+2|}{\sqrt{5}}=\sqrt{(x+2)^{2}+(y-1)^{2}}

Now abscissa of PP is −2⇒x=−2-2 \Rightarrow x=-2

∣y−25∣=0+(y−1)2⇒∣y−2∣5=∣y−1∣\left|\frac{y-2}{\sqrt{5}}\right|=\sqrt{0+(y-1)^{2}} \Rightarrow \frac{|y-2|}{\sqrt{5}}=|y-1|

⇒(y−2)2=5(y−1)2\Rightarrow(y-2)^{2}=5(y-1)^{2}

⇒4y2−6y+1=0⇒\Rightarrow 4 y^{2}-6 y+1=0 \Rightarrow Sum of ordinates

=−(−64)=32=-\left(\frac{-6}{4}\right)=\frac{3}{2}

32\boxed{\frac{3}{2}}

Solution figure

Answer key and solution verified before publishing.

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Exam
JEE Main 2025
Paper
7 April, Morning Shift
Subject
Mathematics
Chapter
Parabola
Topic
Considering a Line or a Point wrt a Parabola