## Question

All chords of the curve which subtend a right angle at the origin always pass through the point

### Solution

(1, –2)

Let *ax* + *by* = 1 be a family of chords of the curve

subtending a right angle at the origin.

The combined equation of the straight lines joining the origin to the points of intersection of and the chord *ax* + *by* =1 is

This represents a pair of perpendicular lines.

#### SIMILAR QUESTIONS

If one of the lines represented by the equation is a bisector of the angle between the lines*xy* = 0, then λ =

If θ is the angle between the straight lines given by the equation , then cosec^{2} θ =

The line *y* = *mx* bisects the angle between the lines

, if

If two pairs of straight lines having equations have one line common then *a* =

The point of intersection of the The Pair of Straight Lines given by

The square of the distance between the origin and the point of intersection of the lines given by

The centroid of the triangle whose three sides are given by the combined equation

If first degree terms and constant term are to be removed from the equation , then the origin must be shifted at the point

The angle between the straight lines joining the origin to the points of intersection of and 3*x* – 2*y* = 1 is

If the pair of lines represented by intersect on y-axis, then