Show that all chords of curve 3x^2 - y^2 - 2x + 4y = 0, which subtend a right angle at the origin pass through a fixed point.

Question 1

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 the point.

Question 2

The given curve is

3x2 - y2 - 2x + 4y = 0 ....(i)

Let y = mx + c be the chord of curve (i) which subtend right angle at origin. Then, the combined equation of lines joining points of intersection of curve (i) and chord y = mx + c to the origin, can be obtained by the equation of the curve homogeneous. ie,

Since, the lines represented are perpendicular to each other.

kratos · Answer 1 · 2020-07-31T09:06:00+0000

The given curve is

3x2 - y2 - 2x + 4y = 0 ....(i)

Let y = mx + c be the chord of curve (i) which subtend right angle at origin. Then, the combined equation of lines joining points of intersection of curve (i) and chord y = mx + c to the origin, can be obtained by the equation of the curve homogeneous. ie,

Since, the lines represented are perpendicular to each other.

Show that all chords of curve 3x^2 - y^2 - 2x + 4y = 0, which subtend a right angle at the origin pass through a fixed point.

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1 Answer

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Show that all chords of curve 3x^2 - y^2 - 2x + 4y = 0, which subtend a right angle at the origin pass through a fixed point.

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1 Answer

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