Elements of analytical geometry and the differential and integral calculus . m ANALYTICAL GEOMETRY. If the same line passes througli the point F, the equation forthat point must be y=:ax-{-b. (2) And the same line passing through Q, the equation for thatpoint must be y=ax-}-h. (3) Subtracting (3) from (2) and we find y—y=a(x—x) (4) for the equation which passes through the two points P and Q* Subtracting (2) from (1) and we have y-^yz=a(x-^x) (5) for the equation of the line which passes through the two pointsP and If. The line which passes through the three points Q, P, and ff^is expressed in
Elements of analytical geometry and the differential and integral calculus . m ANALYTICAL GEOMETRY. If the same line passes througli the point F, the equation forthat point must be y=:ax-{-b. (2) And the same line passing through Q, the equation for thatpoint must be y=ax-}-h. (3) Subtracting (3) from (2) and we find y—y=a(x—x) (4) for the equation which passes through the two points P and Q* Subtracting (2) from (1) and we have y-^yz=a(x-^x) (5) for the equation of the line which passes through the two pointsP and If. The line which passes through the three points Q, P, and ff^is expressed in the two equations (4) and (5). Conceive the line QPJI to revolve on the point P, so as tomake Q coincide with P, then the line will be a tangent at P. We have now to determine the value of a, when the line becomesa tangent at P. Because the two points P and Q are in the circumference, wehave Subtracting and factoring the remainder, gives us (a:+^)(a;-:.)+(/+3/)(/-/)=0. (6) The value of (y—y) taken from (4) and substituted in (6),and then divided by (x—x) will red
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