Find a parametric solution of ( ) 2+ − = 0 as follows. (a) Write an equation for y in terms of = / and show that
= 2+ (2 + 1) .
(b) Using as the independent variable, arrange this as a linear first-order equation for .
(c) Find an appropriate integrating factor to obtain =ln − + (1 − )2 , which, together with the expression for obtained in (a), gives a parameterisation of the solution.
(d) Reverse the roles of and in steps (a) to (c), putting / = −1, and show that essentially the same parameterisation is obtained

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

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