In general two tangents can be drawn from an external point (x1 y1) to the hyperbola and they are
y – y1 = m1 (x - x1) & y -y1 = m2 (x - x1 ), prove that m1 & m2 are roots of the equation
( x1^2-a^2 ) m^2 – ( 2*x1*y1 ) m+y1^2+b^2=0

Question

Arun · Answer

Dear student Just write Equation of chord of contact T = 0 as these contact points lines passes through (x1, y1) hence you get equation in 2 dgree.

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In general two tangents can be drawn from an external point (x1 y1) to the hyperbola and they are y – y1 = m1 (x - x1) & y -y1 = m2 (x - x1 ), prove that m1 & m2 are roots of the equation ( x1^2-a^2 ) m^2 – ( 2x1y1 ) m+y1^2+b^2=0

In general two tangents can be drawn from an external point (x1 y1) to the hyperbola and they are
y – y1 = m1 (x - x1) & y -y1 = m2 (x - x1 ), prove that m1 & m2 are roots of the equation
( x1^2-a^2 ) m^2 – ( 2x1y1 ) m+y1^2+b^2=0

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In general two tangents can be drawn from an external point (x1 y1) to the hyperbola and they are y – y1 = m1 (x - x1) & y -y1 = m2 (x - x1 ), prove that m1 & m2 are roots of the equation ( x1^2-a^2 ) m^2 – ( 2*x1*y1 ) m+y1^2+b^2=0

In general two tangents can be drawn from an external point (x1 y1) to the hyperbola and they arey – y1 = m1 (x - x1) & y -y1 = m2 (x - x1 ), prove that m1 & m2 are roots of the equation( x1^2-a^2 ) m^2 – ( 2*x1*y1 ) m+y1^2+b^2=0