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AP EAMCET202120 Aug 2021Morning ShiftMathematicsStraight LinesActual

A line has slope m and y -intercept 4. The distance between the origin and the line is equal to

Options

  1. A4 1 - m 2
  2. B4 m 2 - 1
  3. C4 m 2 + 1
  4. D4 m 1 + m 2

Correct answer

C. 4 m 2 + 1

Step-by-step solution

Given, the line with slope m and y intercept 4 . As we know by the slope-intercept form of a line, a line with a slope m and y intercept c , the equation of the line is y = m x + c . ⇒ The equation of the line is y = m x + 4 . Also, the distance between a point x 1 , y 1 and a line a x + b y + c = 0 is given by a x 1 + b y 1 + c a 2 + b 2 units. ∴ The distance between origin and the line y = m x + 4 = 4 1 + m 2 .

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