Show that all chords of curve 3x2 – y2 – 2x + 4y = 0, which subtend a right angle at the origin pass through a fixed point. Find the coordinates of that point.
Answers
Answer:
The given curve is 3x2 – y2 – 2x + 4y = 0. ….. (1)
Let y = mx be the chord of the curve (1) which subtends a right angle at the origin. Then, we try to find the points of intersection of the given curve with the chord y = mx + c.
Hence, we have 3x2 – y2 – 2x [(y-mx)/c)] + 4y [(y-mx)/c)] = 0
Hence, 3cx2 – cy2 – 2xy + 2mx2 + 4y2 – 4mxy = 0
This implies (3c + 2m)x2 – 2(1+2m)xy + (4-c)y2 = 0
Now, the lines represented here are perpendicular to each other and hence,
The coefficient of x2 + the coefficient of y2 = 0
This gives, 3c + 2m + 4 – c = 0
Hence, c+m+2 = 0
On comparing with y = mx + c we get that y = mx + c passes through (1, -2).
Hence, the coordinates of the required point are (1, -2).
Answer:
nerve impulse conduction mechanism
Step-by-step explanation:
Hence, we have two relations
(3y-4x+17) = (4y+3x-19)
and (3y-4x+17) = - (4y+3x-19)
This gives y +7x = 36 and 7y-x = 2
Out of these two, the equation of the bisector of ∠ABC is 7y = x + 2.