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Statement 1 : If from any point P(x1, y1...

Statement 1 : If from any point `P(x_1, y_1)` on the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=-1` , tangents are drawn to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1,` then the corresponding chord of contact lies on an other branch of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=-1` Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola.

Text Solution

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Chord of contact of `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` w.r.t. point `P(x_(1),y_(1))` is
`(x x_(1))/(a^(2))-(yy_(1))/(b^(2))=1" (1)"`
Eq. (1) can be written as `(x(-x_(1)))/(a^(2))-(y(-y_(1)))/(b^(2))=-1`, which is tengent to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=-1` at point `(-x_(1),-y_(1))`.
Obviously, points `(x_(1),y_(1)) and (-x_(1),-y_(1))` lie on the different branches of hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=-1`.
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