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Mathematics · Circles

JEE Advanced 2019 — Paper 1 — Question 32

A line y=mx+1y=m x+1 intersects the circle (x−3)2+(y+2)2=25(x-3)^{2}+(y+2)^{2}=25 at the points PP and QQ. If the midpoint

of the line segment PQ has x -coordinate −35-\frac{3}{5}, then which one of the following options is correct?

  1. Option A:

    4≤m<64 \leq \mathrm{m}<6

  2. Option B:

    −3≤m<−1\quad-3 \leq \mathrm{m}<-1

  3. Option C:

    2≤m<42 \leq \mathrm{m}<4

    Correct
  4. Option D:

    6≤m<86 \leq \mathrm{m}<8

Answer: C

Step-by-step solution

PQ⊥OR⇒ Stope OR=−1 m=−35 m+1+2−35−3⇒ m2−5 m+6=0⇒ m=2,3\begin{aligned} & \mathrm{PQ} \perp \mathrm{OR} \Rightarrow \text { Stope } \mathrm{OR}=-\frac{1}{\mathrm{~m}}=\frac{-\frac{3}{5} \mathrm{~m}+1+2}{-\frac{3}{5}-3} \\& \Rightarrow \mathrm{~m}^{2}-5 \mathrm{~m}+6=0 \\& \Rightarrow \mathrm{~m}=2,3 \end{aligned}
Solution figure

Answer key and solution verified before publishing.

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Exam
JEE Advanced 2019
Paper
Paper 1
Subject
Mathematics
Chapter
Circles
Topic
Considering a Line or a Point wrt a Circle

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