If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find dy dx . 1. x = 2at2, y = at4 2. x = a cos q, y = b cos q 3. x = sin t, y = cos 2t 4. x = 4t, y = 4 t 5. x = cos q cos 2q, y = sin q sin 2q 6. x = a (q sin q), y = a (1 + cos q) 7. x = 3 sin cos 2 t t , 3 cos cos2 t y t = 8. cos log tan 2 t x a t = + y = a sin t 9. x = a sec q, y = b tan q 10. x = a (cos q + q sin q), y = a (sin q q cos q) 11. If 1 1 sin cos , , show that t t dy y x a y a dx x
Question 1:x = 2at2, y = at4
Question 2:x = a cos q, y = b cos q
Question 3:x = sin t, y = cos 2t
Question 4:x = 4t, y = 4 t
Question 5:x = cos q – cos 2q, y = sin q – sin 2q
Question 6:x = a (q – sin q), y = a (1 + cos q)
Question 7:x = 3 sin cos 2 t t , 3 cos cos2 t y t =
Question 8:cos log tan 2 t x a t = + y = a sin t
Question 9:x = a sec q, y = b tan q
Question 10:x = a (cos q + q sin q), y = a (sin q – q cos q)
Question 11:If 1 1 sin cos , , show that t t dy y x a y a dx x
