Question

The vertices of a variable triangle are
(3,4) (5 cos 6,5 sin 6) and
(5 sin 0, -5 cos 6), where 0 E R. Then which
of the following is true
(A) Circumcentre of the triangle (0,0)
(B) Locus of orthocentre is
(x + y - 1)² + (x – – 7)2 = 50
(C) Circumcentre of triangle (3, 4)
(D) locus of orthocentre is
(x + y - 7) + (x – y + 1)2 = 100​

Answer 1

Answer:

(-4 , - 3) is orthocenter of  the Triangle formed by the lines X + 2 Y=0,4 x + 3Y -5 =0 and 3 X + Y =0

Step-by-step explanation:

X + 2 Y=0,

4 x + 3Y -5 =0 and

3 X + Y =0

Vertex of these two sides

X + 2 Y=0,

4 x + 3Y -5 =0

4x + 8y  = 4x + 3y - 5

=> 5y = - 5

=> y = -1

x = 2

(2 , -1)

altitude from (2 , -1) on 3X + Y = 0 => Y = -3x

slope = -1/(-3) = 1/3

y = x/3 + c

-1 = 2/3 + c

c = -5/3

y = x/3 - 5/3

3y = x - 5

now similarly

Vertex of these two sides

X + 2 Y=0,

3 X + Y =0

X + 2Y = 6X + 2Y

5X = 0

=> X = 0 , Y = 0

Altitude on 4 x + 3Y -5 =0 =>  y = -4x/3  + 5

Slope of altitude = 3/4

y = 3x/4 + c

0 = 0 + c

y = 3x/4

4y = 3x

3y = x - 5

4y = 3x

4x - 20 = 9x

=> 5x = -20

=> x = - 4

y = - 3

(-4 , - 3) is orthocenter of  the Triangle formed by the lines X + 2 Y=0,4 x + 3Y -5 =0 and 3 X + Y =0

Find the coordinates of the orthocenter of triangle whose vertices are ...

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