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If the line lx+my+n=0 touches the hyperb...

If the line `lx+my+n=0` touches the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`. Then

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If the l x+ my=1 is a normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , then shown that (a^(2))/(l^(2))-(b^(2))/(m^(2))=(a^(2)+b^(2))^(2)

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STATEMENT-1 : The line y = (b)/(a)x will not meet the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1, (a gt b gt 0) . and STATEMENT-2 : The line y = (b)/(a)x is an asymptote to the hyperbola.

Find the condition that line lx + my - n = 0 will be a normal to the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 .

If the lines lx+my+n=0 passes through the extremities of a pair of conjugate diameters of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , show that a^(2)l^(2)-b^(2)m^(2)=0 .

The line y = 4x + c touches the hyperbola x^(2) - y^(2) = 1 if