Question

The line L given by `x/5+y/b=1` passes through the point (13, 32). The line K is parallel to L and its equation is `x/c+y/3=1`. Then, the distance between L and K is ______.

Options

• `23/sqrt15`

• `sqrt17`

• `17/sqrt15`

• `23/sqrt17`

Answer 1

The line L given by `x/5+y/b=1` passes through the point (13, 32). The line K is parallel to L and its equation is `x/c+y/3=1`. Then, the distance between L and K is `underline(23/sqrt17)`.

Explanation:

Line L passes through (13, 32).

`therefore 13/5+32/b=1`

⇒ b = -20

So,equation of L is `x/5-y/20=1`

⇒ 4x - y = 20

Slope of L is m₁ = 4.

Slope of `x/c+y/3=1` is `m_2=-3/c`

`=>-3/c=4`

`=>c=-3/4`

Equation of line K is `-(4x)/3+y/3=1`

⇒ 4x - y = -3

Distance between L and K is `abs((20+3)/sqrt(16+1))=23/sqrt17`