If the line lx+my=1 be a normal to the ...

If the line `lx+my=1` be a normal to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`, show that, `(a^(2))/(l^(2))-(b^(2))/(m^(2))=(a^(2)+b^(2))^(2)`

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If the straight line lx+my=n is a normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 show that (a^(2))/(l^(2))-(b^(2))/(m^(2))=((a^(2)+b^(2))^(2))/(n^(2)) .

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Show that the locus of the midpoints of the chords of the circle x^(2)+y^(2)=a^(2) which are tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is (x^(2)+y^(2))^(2)=a^(2)x^(2)-b^(2)y^(2) .

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If the straight line lx+my+n=0 be a normal to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then by the application of calculus, prove that (a^2)/(l^2)-(b^2)/(m^2)=((a^2+b^2)^2)/(n^2) .

The slope of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( x_(1),y_(1)) is-

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x0, y0).

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