Conics Question (1 Viewer)

Casper_18 · Jun 30, 2009

The points P(cp, c/p) & Q(cq, c/q) lie on the rectangular hyperbola xy = c^2.
The chord PQ subtends a right angle at another point R(cr, c/r) on the hyperbola.

Show that the normal at R is parallel to PQ.

kwabon · Jul 1, 2009

Casper_18 said:
The points P(cp, c/p) & Q(cq, c/q) lie on the rectangular hyperbola xy = c^2.
The chord PQ subtends a right angle at another point R(cr, c/r) on the hyperbola.

Show that the normal at R is parallel to PQ.

i will be back from school, and then scan my solution up, until then stay strong my friend.

x.Exhaust.x · Jul 1, 2009

$Gradient of PQ: \\ mpq = (c/q-c/p)/(cq-cp)\\ = -1/qp \\ Gradient of R(cr,c/r)): x= cr, y= c/r \\ dx/dr= c, dy/dr=-c/r^2 \\ dy/dx=dy/dr.dr/dx \\ dy/dx=-c/r^2.1/c \\ =-1/r^2 \\ m1m2=-1 \\ 1/r^2pq=-1 \\ 1/pq=-r^2 \\ \therefore -1/pq=r^2 \\$

Hence, the normal at R is parallel to PQ.

Conics Question (1 Viewer)

Casper_18

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kwabon

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x.Exhaust.x

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