Home
Class 12
MATHS
Two straight lines rotate about two fixe...

Two straight lines rotate about two fixed points (-a, 0) and (a, 0) in antic clockwise direction. If they start from their position of coincidence such that one rotates at a rate double of the other, then locus of curve is

Text Solution

AI Generated Solution

To find the locus of the curve traced by the two straight lines rotating about the fixed points (-a, 0) and (a, 0) with one line rotating at a rate double that of the other, we can follow these steps: ### Step 1: Define the angles of rotation Let the angle of rotation of the line rotating about (-a, 0) be θ. Therefore, the angle of rotation of the line rotating about (a, 0) will be 2θ. ### Step 2: Set up the coordinates Let P be the point where the two lines intersect, with coordinates (h, k). The coordinates of the fixed points are A(a, 0) and B(-a, 0). ...
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE ENGLISH|Exercise Concept applications 1.1|6 Videos

  • COORDINATE SYSYEM

    CENGAGE ENGLISH|Exercise Concept applications 1.2|8 Videos

  • COORDINATE SYSYEM

    CENGAGE ENGLISH|Exercise Illustration1.67|1 Videos

  • COORDINATE SYSTEM

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE ENGLISH|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

Two rods are rotating about two fixed points in opposite directions. If they start from their position of coincidence and one rotates at the rate double that of the other, then find the locus of point of the intersection of the two rods.

Two straight lines pass through the fixed points (+-a, 0) and have slopes whose products is pgt0 Show that the locus of the points of intersection of the lines is a hyperbola.

Two straight lines pass through the fixed points (+-a, 0) and have slopes whose products is pgt0 Show that the locus of the points of intersection of the lines is a hyperbola.

If the represented by the equation 3y^2-x^2+2sqrt(3)x-3=0 are rotated about the point (sqrt(3),0) through an angle of 15^0 , one in clockwise direction and the other in anticlockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is

If the represented by the equation 3y^2-x^2+2sqrt(3)x-3=0 are rotated about the point (sqrt(3),0) through an angle of 15^0 , on in clockwise direction and the other in anticlockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is (1) y^2-x^2+2sqrt(3)x+3=0 (2) y^2-x^2+2sqrt(3)x-3=0 (3) y^2-x^2-2sqrt(3)x+3=0 (4) y^2-x^2+3=0

If the represented by the equation 3y^2-x^2+2sqrt(3)x-3=0 are rotated about the point (sqrt(3),0) through an angle of 15^0 , on in clockwise direction and the other in anticlockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is y^2-x^2+2sqrt(3)x+3=0 y^2-x^2+2sqrt(3)x-3=0 y^2-x^2-2sqrt(3)x+3=0 y^2-x^2+3=0

The difference of the distances of variable point from two given points (3,0) and (-3,0) is 4. Find the locus of the point.

The line joining two points A(2,0) and B(3,1) is rotated about A in anticlockwise direction through an angle of 15^@ . find the equation of line in the new position. If b goes to c in the new position what will be the coordinates of C.

The line joining two points A(2,0) and B(3,1) is rotated about A in anticlockwise direction through an angle of 15^@ . find the equation of line in the new position. If b goes to c in the new position what will be the coordinates of C.

The line joining two points A(2,0) and B(3,1) is rotated about A in anticlockwise direction through an angle of 15^@ . find the equation of line in the new position. If b goes to c in the new position what will be the coordinates of C.