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Straight Lines and Pair of Straight Lines question

2019 · 12 Jan · Shift 2 · Q35
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Straight Lines and Pair of Straight Lines question

2019 · 12 Jan · Shift 2 · Q35

JEE MainMathematicsStraight Lines and Pair of Straight LinesMCQ+4 / −1
If a straight line passing through the point P(–3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is :
  1. A
    x – y + 7 = 0
  2. B
    4x – 3y + 24 = 0
  3. C
    4x + 3y = 0
  4. D
    3x – 4y + 25 = 0
View written solutionFree

Correct answer: B

  1. Use intercept form of a line

A line cutting the coordinate axes at points A(a,0)A(a,0)A(a,0) and B(0,b)B(0,b)B(0,b) has equation xa+yb=1.\frac{x}{a}+\frac{y}{b}=1.ax​+by​=1.

The intercepted portion between the axes is the segment joining A(a,0)A(a,0)A(a,0) and B(0,b)B(0,b)B(0,b).

  1. Midpoint of the intercepted segment

Since P(−3,4)P(-3,4)P(−3,4) bisects the intercepted portion, PPP is the midpoint of ABABAB.

Midpoint of A(a,0)A(a,0)A(a,0) and B(0,b)B(0,b)B(0,b) is (a2,b2).\left(\frac{a}{2},\frac{b}{2}\right).(2a​,2b​).

So, a2=−3⇒a=−6,\frac{a}{2}=-3 \quad \Rightarrow \quad a=-6,2a​=−3⇒a=−6, b2=4⇒b=8.\frac{b}{2}=4 \quad \Rightarrow \quad b=8.2b​=4⇒b=8.

  1. Form the equation of the line

Substitute a=−6a=-6a=−6 and b=8b=8b=8 into intercept form: x−6+y8=1.\frac{x}{-6}+\frac{y}{8}=1.−6x​+8y​=1.

Multiply by 242424: −4x+3y=24.-4x+3y=24.−4x+3y=24.

Rearrange: 4x−3y+24=0.4x-3y+24=0.4x−3y+24=0.

  1. Match with the options

The equation obtained is 4x−3y+24=0,4x-3y+24=0,4x−3y+24=0, which is Option B.

  1. Verification with stored answer

Stored correct answer: B

Our derived answer: B

Hence, they agree.

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