Show that the equations to the straight lines passing through the point (3,−2) and inclined at 60@ to the line sqrt3x+y=1 are y+2=0 and y−sqrt3x+2+3sqrt3=0.

kennadiceKesezt 2022-09-25 Answered
Show that the equations to the straight lines passing through the point ( 3 , 2 ) and inclined at 60 to the line 3 x + y = 1 are y + 2 = 0 and y 3 x + 2 + 3 3 = 0
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

vidovitogv5
Answered 2022-09-26 Author has 10 answers
Let θ be the angle between two lines whose slopes are m 1 , m 2 . Then we have:
tan θ = | m 1 m 2 1 + m 1 m 2 |
tan θ = | m 1 m 2 1 + m 1 m 2 |
As we know m 1 , we can just plug in the value and get m 2 :
3 = | 3 m 2 1 3 m 2 |
3 3 m 2 = 3 m 2 m 2 = 3
or
3 + 3 m 2 = 3 m 2 m 2 = 0
y + 2 = 0 ( x 3 ) y + 2 = 0
y + 2 = 3 ( x 3 ) y 3 x + 2 + 3 3 = 0
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-08-04
Choose 3 inequalities that form a system whose graph is the shaded region shown above.
A . y 2 B . y 2 C . 7 x 4 y 13 D . 7 x + 2 y 17 E . 7 x 4 y 13 F . 7 x + 2 y 17 G . x 2 H . y 2
asked 2022-07-26
Draw a line l and a point P not on l. Construct a perpendicular to l through P. Describe the construction steps and prove the steps are valid (i.e., that the line you construct is perpendicular to L.
asked 2022-07-16
In the diagram to the right, point P lies on the line y = 3 2 x and is one vertex of square P Q R S. Point R has coordinates ( 5 , 0 ).
a. Find the coordinates of point P.
b. If point R lies on line l, and line I divides quadrilateral P Q R S into two regions of equal area, find the equation for line l.
asked 2022-08-11
Let G = { ( x , f ( x ) ) x  lies between  0  and  1 }
Let ( 1 , 0 ) belong to G.
It is given that tangent vector to G at any point is perpendicular to radius vector at that point.
Is G parabola or ellipse?
asked 2022-11-05
Given triangle A B C , with A B = A C and 2 times(length of inradius) which is equal to the length of exradius of excirle opposite vertex A. Setup the coordinate system in the plane of triangle A B C as follow: Origin at vertex B, positive X-axis along B C and positive Y-axis on the A side of B C. Find the equations of the incircle , excircles and circumcircle.
asked 2022-09-25
How can we draw a triangle give one of its vertex and the orthocentre and circumcentre?
asked 2022-08-15
Why do formal mathematics courses teach vector,coordinate geometry and complex numbers separetely?

New questions