A and B are fixed points such that AB=2a. The vertex C of `DeltaABC` such that `cotA+cotB`=constant. Then locus of C is
A
straight line perpendicular to AB
B
straight line parallel to AB
C
circle
D
none of these
Text Solution
Verified by Experts
The correct Answer is:
B
`cot A +cotB=` constant `rArr (AD)/(CD)+(BD)/(CD)=` constant, (where D is the foot of perpendicular from C to AB) `rArr (AD+BD)/(CD) =` constant `rArr (2a)/(CD) =` constant `rArr CD =` constant C is moving at a constant distance from AB `:.` locus of C is a line parallel to AB
Given two points A and B. If area of triangle ABC is constant then locus of point C in space is
In triangle ABC, base BC is fixed. Then prove that the locus of vertex A such that tan B+tan C= Constant is parabola.
Base BC of triangle ABC is fixed and opposite vertex A moves in such a way that tan.(B)/(2)tan.(C)/(2) is constant. Prove that locus of vertex A is ellipse.
Find the locus of the point of intersection of tangents in the parabola x^2=4a xdot which are inclined at an angle theta to each other. Which intercept constant length c on the tangent at the vertex. such that the area of A B R is constant c , where Aa n dB are the points of intersection of tangents with the y-axis and R is a point of intersection of tangents.
In DeltaABC , if AB = c is fixed, and cos A + cosB + 2 cos C = 2 then the locus of vertex C is
a triangle A B C with fixed base B C , the vertex A moves such that cosB+cosC=4sin^2(A/2)dot If a ,ba n dc , denote the length of the sides of the triangle opposite to the angles A , B ,a n dC , respectively, then (a) b+c=4a (b) b+c=2a (c) the locus of point A is an ellipse (d) the locus of point A is a pair of straight lines
A variable plane passes through a fixed point (a ,b ,c) and cuts the coordinate axes at points A ,B ,a n dCdot Show that eh locus of the centre of the sphere O A B Ci s a/x+b/y+c/z=2.
Statement 1 : In a triangle A B C , if base B C is fixed and the perimeter of the triangle is constant, then vertex A moves on an ellipse. Statement 2 : If the sum of the distances of a point P from two fixed points is constant, then the locus of P is a real ellipse.
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.
CENGAGE-COORDINATE SYSTEM-Multiple Correct Answers Type
