Show that the curve x 7 cos t y 4 sin t cos t has two tangents at 0 0 and find their equations Enter your answers as a comma separated list Since x 7 cos t and y 4 sin t cos t we have the following dx dt dy dt m At the point 0 0 we know that cos t 0 y X At the smallest of these values Graph the curve dx which only occurs at odd and ddy so dx V At the largest of these values found to meet the condition in 0 2 dx ddy SO o dx dt dt dx Thus there are two tangents to the curve x 7 cos t y 4 sin t cos t and their equations are as follows Enter your answers as a comma separated list multiples of On the interval 0 27 this only occurs at the following values Enter your answers as a comma separated list and