Question:

A line, with the slope greater than one, passes through the point A (4,3) and intersects the line x-y-2=0 at the point B If the length of the line segment AB is \(\frac{\sqrt{29}}{3},\) then B also lies on the line :

Updated On: Mar 20, 2025
  • 2 x+y=9
  • 3 x-2 y=7
  • x+2 y=6
  • 2 x -3 y =3
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The Correct Option is C

Solution and Explanation

The correct option is(C): x+2 y=6.
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Concepts Used:

Conic Sections

When a plane intersects a cone in multiple sections, several types of curves are obtained. These curves can be a circle, an ellipse, a parabola, and a hyperbola. When a plane cuts the cone other than the vertex then the following situations may occur:

Let ‘β’ is the angle made by the plane with the vertical axis of the cone

  1. When β = 90°, we say the section is a circle
  2. When α < β < 90°, then the section is an ellipse
  3. When α = β; then the section is said to as a parabola
  4. When 0 ≤ β < α; then the section is said to as a hyperbola

Read More: Conic Sections