X
xwrathbringerx
Guest
Hi guys
How do i do these questions:
1. PN is the perpepndicular to an asymptote from a point on a rectangular hyperbola. Prove that the locus of the midpoint of PN is a rectangular hyperbola with the same asymptotes.
2. Prove that the locus of midpoints of parallel chords of xy = c^2 is a diameter.
3. P is a variable point on xy=c^2. The tangent at P cuts the x axis at A and y axis at B. Q is the fourth vertex of OAQB. Show that the locus of Q is xy = 4c^2.
How do i do these questions:
1. PN is the perpepndicular to an asymptote from a point on a rectangular hyperbola. Prove that the locus of the midpoint of PN is a rectangular hyperbola with the same asymptotes.
2. Prove that the locus of midpoints of parallel chords of xy = c^2 is a diameter.
3. P is a variable point on xy=c^2. The tangent at P cuts the x axis at A and y axis at B. Q is the fourth vertex of OAQB. Show that the locus of Q is xy = 4c^2.