Home
Class 12
MATHS
The coordinates of the vertices Ba n dC ...

The coordinates of the vertices `Ba n dC` of a triangle `A B C` are (2, 0) and (8, 0), respectively. Vertex `A` is moving in such a way that `4tanB/2tanC/2=1.` Then find the locus of `A`

A

`((x-5)^(2))/(25)+(y^(2))/(16)=1`

B

`((x-5)^(2))/(16)+(y^(2))/(25) =1`

C

`((x-5)^(2))/(25)+(y^(2))/(9) =1`

D

`((x-5)^(2))/(9)+(y^(2))/(25)=1`

Text Solution

Verified by Experts

The correct Answer is:
A
`4 tan.(B)/(2) tan. (C )/(2) =4 sqrt(((s-a)(s-c))/(s(s-b))) sqrt(((s-a)(s-b))/(s(s-c))) =1`
`rArr 4 ((s-a))/(s) =1`
`rArr s = (4a)/(3) = 4 xx (6)/(3) =8`
Now `2s =a +b+c = 16`
`rArr b +c = 10`
Hence locus is an ellipse having center `-= (5,0)`
`2ae = 6`
And `2a = 10`
`b^(2) = a^(2) - a^(2)e^(2) =25 -9 = 16`
`:.` Equation of ellipse is `((x-5)^(2))/(25) +(y^(2))/(16) =1`,
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

  • ELLIPSE AND HYPERBOLA

    CENGAGE|Exercise Question Bank|1 Videos

Similar Questions

Explore conceptually related problems

If the vertices A,B, C of a triangle ABC are (1,2,3),(-1, 0,0), (0, 1,2), respectively, then find angle ABC .

The vertices A, B, C of a triangle are (2, 1), (5, 2) and (3, 4) respectively. Then the circumcentre is

If the coordinates of the vertices of triangle A B C are (-1,6),(-3,-9) and (5,-8) , respectively, then find the equation of the median through Cdot

Find the coordinates of centroid of the triangle with vertices: (6, 2), (0, 0) and (4, -7)

Find the coordinates of circumcentre of a triangle whose vertices are (-3, 1), (0, -2) and (1, 3)

Find the area of the triangle vertices are (0, 0), (3, 0) and (0, 2)

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.

The equations of the perpendicular bisectors of the sides A Ba n dA C of triangle A B C are x-y+5=0 and x+2y=0 , respectively. If the point A is (1,-2) , then find the equation of the line B Cdot

The coordinates of the point Aa n dB are (a,0) and (-a ,0), respectively. If a point P moves so that P A^2-P B^2=2k^2, when k is constant, then find the equation to the locus of the point Pdot

Find the area of the triangle vertices are (2, 3) (-1, 0), (2, -4)