Q. 34.8( 5 Votes )
Find the equation of the line whose perpendicular distance from the origin is 4 units and the angle which the normal makes with the positive direction of x–axis is 15°.
Answer :
Given: p = 4, α = 15°
Concept Used:
Equation of line in normal form.
Explanation:
We know that, cos 15° = cos (45° – 30°) = cos45°cos30° + sin45°sin30°
cos(A – B) = cosAcosB + sinAsinB
And sin 15 = sin (45° – 30°) = sin 45° cos 30° – cos 45° sin 30°
sin (A – B) = sinAcosB – cosAsinB
So, the equation of the line in normal form is
Formula Used: x cos α + y sin α = p
⇒ (√3 + 1)x + (√3 – 1)y = 8√2
Hence, the equation of line in normal form is (√3 + 1)x + (√3–1)y = 8√2
Rate this question :
Various Forms of Equations of lineFREE Class
Parametric Equations of Straight line48 mins
General Equation of a lineFREE Class
Straight line | Analyse your learning through quiz56 mins
Slope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of lineFREE Class
Motion in a Straight Line - 0372 mins
Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 1063 mins
A vertex of a square is at the origin and its one side lies along the line 3x – 4y – 10 = 0.
Find the area of the square.
RS Aggarwal - Mathematics
Find all the points on the line x + y = 4 that lie at a unit distance from the line 4x+3y=10.
RS Aggarwal - MathematicsThe distance between the orthocenter and circumcentre of the triangle with vertices (1, 2) (2, 1) and 
is
What are the points on the x-axis whose perpendicular distance from the line 
is 4 units?
Find the equation of a line for which
p = 8, α = 225°
RD Sharma - MathematicsFind the equation of a line for which
p = 4, α = 150°
RD Sharma - MathematicsArea of the triangle formed by the points ((a + 3)(a + 4), a + 3), ((a + 2)(a + 3), (a + 2)) and ((a + 1)(a + 2), (a + 1)) is
RD Sharma - MathematicsThe coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y – 11 = 0 are
RD Sharma - Mathematics