Find equation of the line parallel to the line \(3x - 4y + 2 = 0\) and passing through the point (-2, 3).

Question

If the image of the point \( P(1, 2, a) \) in the line \[ \frac{x - 6}{3} = \frac{y - 7}{2} = \frac{7 - z}{2} \] is \( Q(5, b, c) \), then \( a^2 + b^2 + c^2 \) is equal to

Answer 1

The equation of the given line is
\(3x – 4y + 2 = 0\)

or \(y = \frac{3x}{4} +\frac{ 2}{4}\)

\(y=\frac{ 3x}{4} + \frac{1}{2}\), which is of the form \(y = mx + c \)

∴ Slope of the given line=\(\frac{3}{4}\)
It is known that parallel lines have the same slope.

∴ Slope of the other line \(=m=\frac{3}{4}\)
Now, the equation of the line that has a slope of \(\frac{3}{4}\) and passes through the point (-2, 3) is
\(y – 3 = \frac{3}{4} (x – (-2))\)
\(4y – 12 = 3x + 6\)
\(i.e,3x – 4y + 18 = 0\)

Find equation of the line parallel to the line \(3x - 4y + 2 = 0\) and passing through the point (-2, 3).

Solution and Explanation

Top Questions on Distance of a Point From a Line

Questions Asked in CBSE Class XI exam