Having given the bases and the sum of th...

Having given the bases and the sum of the areas of a number of triangles which have a common vertex, show that the locus of the vertex is a straight line.

Text Solution

AI Generated Solution

Topper's Solved these Questions

SEQUENCES AND SERIES
CENGAGE ENGLISH|Exercise All Questions|508 Videos
TRIGONOMETRIC FUNCTIONS
CENGAGE ENGLISH|Exercise All Questions|983 Videos

Similar Questions

Explore conceptually related problems

Given the base BC of the triangle ABC and if angleC-angleB=k, a constant, show that the locus of the vertex A is a hyperbola.

If two isosceles triangles have a common base, prove that the line joining their vertices bisects them at right angles.

The locus of vertices of all isosceles triangles having a common base.

If on a given base B C , a triangle is described such that the sum of the tangents of the base angles is m , then prove that the locus of the opposite vertex A is a parabola.

The number of lines of symmetry which a triangle cannot have is

If the base of a triangle and the ratio of tangent of half of base angles are given, then identify the locus of the opposite vertex.

The ends of the hypertenuse of right angled triangle are ( 0 , 6 ) , (6, 0 ) . The locus of the third vertex is

One vertex of a triangle of given species is fixed and another moves along circumference of a fixed circle. Prove that the locus of the remaining vertex is a circle and find its radius.

CENGAGE ENGLISH-STRAIGHT LINES-All Questions

Find the locus of the point at which two given portions of the straigh...
Text Solution
|
Find the equation of the perpendicular bisector of the line segment ...
Text Solution
|
Having given the bases and the sum of the areas of a number of tria...
Text Solution
|
Find the equation of a line that has y-intercept 4 and is a perpendi...
Text Solution
|
Find the equations of the diagonals of the square formed by the lines ...
Text Solution
|
Find the equation of the straight line that passes through the point (...
Text Solution
|
Find the equation of the line which is parallel to 3x-2y+5=0 and passe...
Text Solution
|
Consider two lines L1a n dL2 given by a1x+b1y+c1=0a n da2x+b2y+c2=0 ...
Text Solution
|
Find the locus of a point P which moves such that its distance from th...
Text Solution
|
Consider two lines L1a n dL2 given by x-y=0 and x+y=0 , respectively, ...
Text Solution
|
In what ratio does the line joining the points (2,3) and (4,1) divide ...
Text Solution
|
Show that the lines 4x+y-9=0,x-2y+3=0,5x-y-6=0 make equal intercepts o...
Text Solution
|
Find the equation of the bisector of the obtuse angle between the line...
Text Solution
|
Show that if any line through the variable point A(k+1,2k) meets the l...
Text Solution
|
The incident ray is along the line 3x-4y-3=0 and the reflected ray is ...
Text Solution
|
If the line y =sqrt(3)x cuts the curve x^3+y^3+3x y+5x^2+3y^2+4x+5y-1=...
Text Solution
|
about to only mathematics
Text Solution
|
The area of a parallelogram formed by the lines a x+-b y+-c=0 is (a)(c...
Text Solution
|
The vertices Ba n dC of a triangle A B C lie on the lines 3y=4xa n dy=...
Text Solution
|
If each of the points (x1,4),(-2,y1) lies on the line joining the poi...
Text Solution
|