First slide
Hyperbola in conic sections
Question

If the chords of contacts of the tangents from the points

x1, y1 and x2, y2 to the hyperbola 2x23y2=6

are at right angle, then 4x1x2+9y1y2 is equal to

Moderate
Solution

Equation of the chords of contacts are

2xx13yy1=6,2xx23yy2=6

Since they are at right angles  2x13y1×2x23y2=1

 4x1x2+9y1y2=0.

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