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AP EAMCET · Maths · Straight Lines

Match the following
List - I
A) The equation of line passing through \((4,3)\) whose \(\mathrm{X}\)-intercept is twice its Y-intercept
B) The equation of the line passing through the centroid and circumcentre of \(\triangle A B C\) with vertices \(\mathrm{A}(1,1), \mathrm{B}(3,3), \mathrm{C}(6,-6)\)
C) The equation of the line whose \(\mathrm{X}\)-intercept is \((-3 / 5)\)
III) \(x+2 y+\sqrt{2}=0\) and is perpendicular to \(x-y+2=0\)
D) The equation of the line whose distance from the origin is 2 and the normal drawn from the origin makes an angle \(45^{\circ}\) with the positive direction of \(\mathrm{X}\)-axis
List - II
I) \(x+y-2 \sqrt{2}=0\)
II) \(7 x+23 y-8=0\)
IV) \(x+2 y-10=0\)
IV) \(x+2 y-10=0\)
V) \(5 x+5 y+3=0\)
The correct answer is

  1. A \[
    \begin{array}{cccc}
    \text { A } & \text { B } & \text { C } & \text { D } \\
    \text { (V) } & \text { (IV) } & \text { (II) } & \text { (I) } \\
    \end{array}
    \]
  2. B \[
    \begin{array}{cccc}
    \text { A } & \text { B } & \text { C } & \text { D } \\
    \text { (III) } & \text { (V) } & \text { (IV) } & \text { (II) }\\
    \end{array}
    \]
  3. C \[
    \begin{array}{cccc}
    \text { A } & \text { B } & \text { C } & \text { D } \\
    \text { (IV) } & \text { (II) } & \text { (V) } & \text { (I) }\\
    \end{array}
    \]
  4. D \[
    \begin{array}{cccc}
    \text { A } & \text { B } & \text { C } & \text { D } \\
    \text { (II) } & \text { (I) } & \text { (III) } & \text { (V) }\\
    \end{array}
    \]
Verified Solution

Answer & Solution

Correct Answer

(C) \[
\begin{array}{cccc}
\text { A } & \text { B } & \text { C } & \text { D } \\
\text { (IV) } & \text { (II) } & \text { (V) } & \text { (I) }\\
\end{array}
\]

Step-by-step Solution

Detailed explanation

Line intercept form: \(\frac{x}{a} + \frac{y}{b} = 1\) Given \(a = 2b\): \(\frac{x}{2b} + \frac{y}{b} = 1 \implies x + 2y = 2b\) Passes through \((4,3)\): \(4 + 2(3) = 2b \implies 10 = 2b \implies b=5\) Equation: \(x + 2y = 2(5) \implies x + 2y - 10 = 0\) This matches with List…